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We have investigated absorption losses due to surface water adsorbed on the surface of silicon heterostructure nanocavities with quality (Q) factors of several million. Measurements performed while changing the ambient humidity that the nanocavity is exposed to show that the Q value depends linearly on humidity. We also reveal that chemical treatment to change the degree of hydrophilicity of the surface results in a drastic increase of Q; we have obtained an experimental value of 9 million, which represents a new record for a heterostructure nanocavity. We analytically determine the absolute value of absorption loss by exploiting the degree of fluctuation of Q values between different samples.
© 2014 Optical Society of America
1. Introduction
Optical resonators with high quality (Q) factors and small volumes (V) have attracted much attention because high Q/V ratios yield strong light-matter interactions. This is beneficial for optical devices, resulting in high sensitivity, low operating energies, enhancement of nonlinear optical phenomena, and controllable emission rates. High-Q nanocavities in two-dimensional (2D) photonic crystal (PC) slabs possess exceptionally small volumes approaching one cubic wavelength [1–6]. In particular, Q values of larger than one million have been achieved in silicon (Si) nanocavities [6–11]. This has recently led to the realization of various exotic devices [12–16]. Further enhancement of these Q factors will extend the potential of such nanocavities toward novel applications.
We have devoted much effort to increasing the experimental Q factors (Qexp) of Si nanocavities. The highest value of 3.9 million reported thus far was achieved for a heterostructure nanocavity [8]. However, the theoretical Q factor (Qdes) of this cavity is more than 10 million. This discrepancy between Qexp and Qdes is attributed to imperfections in the fabricated cavities, which give rise to an additional Q factor (Qimp). In other words, the Qexp values of our most recently studied nanocavities are largely determined by Qimp. In order to increase Qexp, losses due to these imperfections should be minimized.
We have performed analytical studies to show that the sources of Qimp can be divided into two categories: scattering loss due to structural variations in the air holes and absorption loss related to the surface [17]. Our recent work on increasing Qexp has focused on reducing the scattering loss [7,8,18] because it was suspected to be larger than the absorption loss, the origins of which for a long time remained unclear. However, studies of our most recent high-Q nanocavities revealed that the absorption loss can be of equal magnitude to the scattering loss [8]. We also obtained direct indications that water (H2O) adhering to the Si surface could be one of the main causes of the absorption loss [9]. It is known that surface water adsorption is an important loss factor in silica microspheres [19,20] and silica toroid microcavities [21]. Although nanocavities have larger surface area to volume ratios, the effect of surface water has not been investigated experimentally.
In this article we report on a study of absorption loss due to surface water adsorption on Si high-Q heterostructure nanocavities. First, we measured the dependence of Qexp on the ambient humidity. A Qexp value of 5.1 million was obtained for a nanocavity at a relative humidity (RH) of less than 5%, which was reduced to 4.5 million at RH = 74%. Second, we investigated the effect on Qexp of chemical treatment to remove a thin Si-oxide layer at the surface. This resulted in a drastic increase of Qexp to a maximum value of 9 million.
2. Analysis of Qexp and Qimp factors for major types of nanocavities
Over the last decade we have increased Qexp by more than three orders of magnitude by improving both the design of cavities and their fabrication process [1–4,7,8]. Figure 1 shows the most important of these advances: results for an L3 nanocavity with three missing air holes [2], a hole-shifted L3 nanocavity [3], a double-heterostructure (DH) nanocavity [4], and multi-heterostructure (MH) nanocavities [7,8]. The values of Qdes were calculated using the three-dimensional (3D) finite-difference time-domain (FDTD) method. The values of Qexp are smaller than Qdes for all nanocavities due to Qimp, according to the following relation:
Fig. 1 Improvements in Qdes (squares) and Qexp (triangles) for major types of nanocavities (left-hand axis). The right-hand axis shows the optical loss 1/Qexp, split into its components 1/Qdes and 1/Qimp.
The reciprocal Q values are the optical losses; we use them to discuss the mechanisms by which Qexp is reduced. The bars in Fig. 1 show the experimental loss (1/Qexp) for each nanocavity, divided into the design loss (1/Qdes) and the imperfection loss (1/Qimp). It can be seen that a reduction of 1/Qimp would significantly increase Qexp in our most recently reported nanocavity [8]. Similar scenarios have been reported for other types of high-Q PC cavities [10,11,22–24]. As explained above, 1/Qimp is the sum of the scattering loss (1/Qscat) and the absorption loss (1/Qabs) as follows:
In the following, we focus on reducing the value of 1/Qabs.3. Sample structure and experimental setup
Figure 2(a) shows a schematic picture of the heterostructure nanocavity studied in the current work. The PC consisted of a triangular lattice of circular air holes with radii of 110 nm, formed in a 220-nm-thick Si slab. The nanocavity was formed by a line defect of 17 missing air holes where the lattice constant in the x-direction was increased every two periods by an amount Δa: a2 = a1 + Δa, a3 = a1 + 2Δa. We prepared two types of samples with Qdes ≈58 million and Qdes ≈20 million. The cavities were separated from the excitation waveguides by 8 rows of air holes in the measured samples. The additional Q factor (Qin) determined by the coupling to the waveguide was calculated to be ~1.4 × 108 by the 3D FDTD method, which is included in the above Qdes values. All samples were fabricated using the procedure previously reported in [9]. Special care was taken to keep the surface clean throughout the fabrication process. Nevertheless, a large number of H2O molecules can still adhere to the surface. This is because the fabricated samples were kept in a standard desiccator with RH = 30−40% for several months, resulting in oxidation of the Si surface to SiOx (x < 2). The SiOx surface layer is more hydrophilic than Si because the oxygen atom has larger electronegativity.
Fig. 2 (a) Schematic picture of the nanocavity studied here, created by a two-step heterostructure. The positions of the colored air holes are shifted with respect to those in the main PC lattice. (b) Experimental setup for time-domain measurements. SMF: single mode fiber. MMF: multi mode fiber. EOM: electro-optical modulator. OL: objective lens.
Figure 2(b) shows the measurement system used. Samples were placed in an isolation chamber in which the ambient humidity was controlled using dry nitrogen gas (N2) and a water bubbler. We performed time-domain measurements as outlined in Fig. 2(b) to evaluate the lifetimes of the photons (τ) trapped in the nanocavities. The Qexp of the cavity was estimated according to the relation Qexp = ωτ. Rectangular input light pulses were set to a width of 10 ns and a repetition rate of 10 MHz using a pulse generator and electro-optical modulator. The time-domain evolution of emission from the nanocavities was measured using a photomultiplier tube by applying the time-correlated single-photon counting method. Details of this measurement have been described previously [6].
4. Dependence of Qexp on the ambient humidity
In order to confirm that absorption loss due to surface water occurs, we investigated the effect on Qexp of changing the ambient humidity. We used the nanocavity with Qdes ≈58 million, a higher value than for the cavities used in our previous studies so that changes in 1/Qabs would be more prominent. The parameters of this heterostructure were a1 = 425 nm, Δa = 3 nm, and a resonant wavelength (λcav) of ~1630 nm. The green air holes in Fig. 2(a) were shifted outward in the y-direction by 4.25 nm and the red air holes were shifted outward in the x-direction by 8.50 nm, according to a method reported elsewhere [25]. First, we measured the sample in standard air with RH = 38%, obtaining a Qexp of 4.86 million. These were the standard measurement conditions used in our previous reports [6–8]. Second, the chamber was filled with dry N2, reducing the RH to < 5%. We measured the same nanocavity 30 minutes after this air replacement, which resulted in an increase of Qexp to 5.09 million. Third, the chamber was filled with humid N2, increasing the RH to 74%. The measurement was carried out using the same procedure, yielding a Qexp of 4.48 million. Finally, the chamber was filled again with dry N2 and Qexp returned to 5.08 million.
Table 1 summarizes these results and Fig. 3 shows the relation between the humidity and 1/Qimp calculated using Eq. (1). It is seen that 1/Qimp increases linearly with humidity. This dependence is most likely caused by the adsorption and desorption of H2O molecules on the surface. The increase of 1/Qimp between RH values of 5% and 74% is 2.68 × 10−8, corresponding to an increase of 1/Qabs. We quantitatively evaluate this increase as representing the number of surface H2O molecules adsorbed.
Table 1. Summary of measurements of the humidity dependence of Qexp. Experiments were carried out in chronological order from left to right with a waiting time of 30 minutes between each.
Fig. 3 Humidity dependence of imperfection loss (1/Qimp) of a nanocavity. The dashed line is a linear fit to the measured data. The inset shows a model for the adsorption of surface water.
We assume that the H2O molecules are uniformly adsorbed on the top and bottom surfaces of the slab and on the inner walls of the holes as illustrated in Fig. 3. The magnitude of 1/Qabs can be evaluated from the following equation:
where α and n are the absorption coefficient and the refractive index. We used values of α = 6.4 cm−1 and n = 1.31 for liquid H2O at λcav = 1.63 μm [26]. The parameter η is an effective conversion factor based on the surface water volume to cavity volume ratio: η = S × Twater/Vcav, where S is the effective surface area, Twater is the thickness of the H2O layer, and Vcav is the cavity volume. We approximated the area of nanocavity as the rectangular with dimensions at the center of cavity and assumed that the electromagnetic field is uniformly distributed in the x−y plane. Taking into account that the electric field intensities at the top and bottom surfaces are 50% of that at the center of the slab, S and Vcav were calculated as 9.46 × a12 and 3.59 × a13, respectively. Under these assumptions, the increase of Twater that occurred when the RH was raised from 5% to 74% was evaluated to be 3.41 × 10−2 nm. Approximating the volume of a H2O molecule to be 29.9 Å3 (molar volume /Avogadro constant), the number of H2O molecules that were newly adsorbed on the cavity surface on increasing the RH was estimated to be 1.95 × 106. This value corresponds to 1.14 H2O molecules per nm2.5. Drastic increase of Qexp by chemical treatment
It is known that once H2O molecules are adsorbed on a SiOx surface, they are not completely desorbed by decreasing the humidity [27,28]. Therefore, we next investigated the effect on Qexp of applying chemical treatment to remove the thin SiOx layer at the surface. In this experiment, we used the nanocavity with Qdes ≈20 million. The parameters for this heterostructure were as follows: a1 = 410 nm, Δa = 4 nm, and λcav ≈1570 nm. These values are similar to those used in our previous statistical study [8]. We measured nine nanocavities with the same structure, all integrated on the same chip. First, we measured Qexp in dry N2 with RH < 5%. The results are summarized in the upper row of Table 2.The average (Avg.) and standard deviation (S.D.) of the nine measured 1/Qimp values are shown in the two right-hand columns. These values are slightly larger than those for our previous study performed in standard air [8], which implies that the sample quality in the current experiment is relatively low.
Table 2. Summary of statistical measurements on nine nanocavities before and after DHF treatment. Three cavities were not measured after the process. The labels Avg. and S.D. refer to the average and standard deviation, respectively.
After the measurements above, the chip was dipped into dilute hydrofluoric acid (DHF) to remove the thin SiOx layer. It was then rinsed with deionized water and dried by a stream of N2. After this process most of the surface was terminated with hydrogen atoms. Such a surface is known to be more hydrophobic than SiOx because hydrogen has a similar electronegativity to Si. The sample was placed in the chamber within 5 minutes of completing the chemical process, then the chamber was quickly filled with dry N2 to prevent H2O molecules from adhering to the surface. The same measurement was performed as before the chemical treatment. The results are summarized in the lower row of Table 2. We were unable to measure three of the prepared cavities due to adventitious errors resulting from the chemical process. Table 2 shows that a drastic increase in Qexp occurred for all the measured cavities. We note that Qexp decreased almost to the initial values when the chip was left in a standard air environment for a few days. Therefore, this increase of Qexp does not originate from a decrease of 1/Qscat but rather from a decrease of 1/Qabs. In other words, the magnitude of variation of the air hole structure is not changed by the chemical treatment.
It should be emphasized that the relative magnitudes of Qexp between the 6 cavities that were measured twice were essentially unchanged by the treatment. This result indicates that the adsorption of surface water added similar 1/Qabs values to all the cavities. In other words, the variation in 1/Qimp, namely S.D.(1/Qimp), can mainly be attributed to fluctuations of 1/Qscat resulting from random air hole variations, as we have suggested in previous reports [8,18]. Exploiting this property using 3D FDTD simulations that take the air hole variations into account, we were able to determine the average value of 1/Qscat for the nine measured cavities and finally derive the absolute value of 1/Qabs.
In this calculation, random nanometer-scale variations in the positions and radii were applied to all the air holes such that the probability of variations followed a normal distribution with a standard deviation of σhole. Because the calculated Q values are strongly dependent on the fluctuation pattern, we performed the calculation for 30 different fluctuation patterns. This statistical simulation yielded the following relations for the average value and standard deviation of 1/Qscat (details of the calculations are given in [18]):
Figure 4(a) shows a contour map of the appearance frequency of 1/Qscat as a function of σhole, with lines superimposed to represent the above values of Avg.(1/Qscat) and ± S.D.(1/Qscat). Comparison with these simulation results gives σhole = 0.47 nm and Avg.(1/Qscat) = 1.65 × 10−7 for the measured samples. Therefore, the absolute value of 1/Qabs before chemical treatment was determined as 1.24 × 10−7 from Eq. (2). Although S.D.(1/Qimp) decreased after the DHF process as shown in Table 2, this might be due to the accidental loss of the two samples (No.4 and No.7) that had the lowest Qexp before the process. The value of S.D.(1/Qimp) should be the same before and after DHF treatment because this process does not change the magnitude of σhole. Therefore, a more realistic estimate of the 1/Qabs after the treatment is 0.13 × 10−7.
Fig. 4 (a) Calculated contour map of the appearance frequency of scattering loss as a function of σhole. The white arrow shows the experimental S.D.(1/Qimp) before chemical treatment. Schematic views on the right show variation in the air hole radius (dr) and position (dx, and dy). (b) Breakdown of average 1/Qexp before and after removing the surface SiOx layer. The numbers on the bars indicate the magnitudes of each type of loss. The schematic picture on the right shows the DHF treatment process.
Figure 4(b) presents the breakdown of the average (1/Qexp) before and after the DHF process. The contribution of 1/Qabs to 1/Qexp was reduced to 5.7% by removing the SiOx layer. Using Eq. (3), the reduction in Twater was 9.79 × 10−2 nm where α = 9.4 cm−1 at 1570 nm [26]. If 1/Qabs is completely attributed to the surface water, it can be concluded that 4.24 H2O molecules/nm2, corresponding to Qabs of 7.2 million, are adsorbed on the surface of the Si nanocavity sample if it is kept in standard air with RH = 40%. Using the adsorption cross-section of the H2O molecule of 0.125 nm2 in the Brunauer–Emmett–Teller (BET) theory [29], it is estimated that 53% of the surface is covered by H2O molecules. This estimation almost agrees with that obtained by mass measurement (80% coverage) for a natural SiO2/Si(100) surface [28]. Therefore, we suspect that the adsorption of surface water represents the main contribution to 1/Qabs for our cavities. (It should be noted that the α for surface water may be smaller than that for bulk water in the wavelengths close to 1600 nm because of the weak hydrogen bond. In addition, the amount of the surface water strongly depends on the preparation method for Si oxide layer [27,28,30]. Therefore, the estimations of Twater have some uncertainty.) It is also possible that absorption by interface states between the Si and SiOx plays a role [31]. Measurements using a dry O2 atmosphere after DHF treatment should clarify this issue.
Finally, we applied DHF chemical treatment to several other chips. Figure 5 shows the time response for the nanocavity that demonstrated the longest measured photon lifetime of 7.54 ns. This lifetime corresponds to a Qexp of 9.05 million, which is 2.3 times larger than the previous record value. Here, we used the nanocavities with Qdes ≈20 million, which were of lower quality than those measured in our previous work [8]. We thus believe that a Qexp exceeding 10 million will be obtained in the near future using nanocavities with improved Qdes and fabrication accuracy.
Fig. 5 Time-resolved signals for input pulsed light (black) with a width of 10 ns and for the nanocavity (red) that showed the longest photon lifetime of 7.54 ns. Similar signals for the previous nanocavities are seen in [6,7].
7. Summary
We have investigated the optical loss that results from surface water adsorbed on Si heterostructure nanocavity samples. We have shown that the Qexp factor depends on the ambient humidity, which indicates that the absorption loss caused by surface water is significant. We have demonstrated that the absorption loss is drastically reduced by applying chemical treatment to remove a thin SiOx layer at the surface. As a result, we have achieved a Qexp of 9 million, the highest value yet for PC cavities. Furthermore, we have estimated the absolute value of the absorption loss due to surface water with the assistance of FDTD simulations, which clarify that the additional Qabs factor about 7 million exists in standard Si high-Q nanocavities. These results represent great steps toward a Qexp of more than 10 million and provide valuable information for the design of other Si photonics devices. Our study also provides important information for applications that utilize the surface such as sensors with high sensitivity.
Acknowledgments
We thank M. Takeuchi for helpful discussion regarding surface water, T. Nakamura for helpful comment in nanocavity design. This work was supported by JSPS KAKENHI (grant numbers 20226002 and 23686015), MEXT KAKENHI (grant numbers 23104721), Future Pioneering Projects, and CPHoST program.
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