## Abstract

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 (*Q*_{exp}) 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 (*Q*_{des}) of this cavity is more than 10 million. This discrepancy between *Q*_{exp} and *Q*_{des} is attributed to imperfections in the fabricated cavities, which give rise to an additional *Q* factor (*Q*_{imp}). In other words, the *Q*_{exp} values of our most recently studied nanocavities are largely determined by *Q*_{imp}. In order to increase *Q*_{exp}, losses due to these imperfections should be minimized.

We have performed analytical studies to show that the sources of *Q*_{imp} 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 *Q*_{exp} 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 (H_{2}O) 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 *Q*_{exp} on the ambient humidity. A *Q*_{exp} 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 *Q*_{exp} of chemical treatment to remove a thin Si-oxide layer at the surface. This resulted in a drastic increase of *Q*_{exp} to a maximum value of 9 million.

## 2. Analysis of *Q*_{exp} and *Q*_{imp} factors for major types of nanocavities

Over the last decade we have increased *Q*_{exp} 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 *Q*_{des} were calculated using the three-dimensional (3D)
finite-difference time-domain (FDTD) method. The values of *Q*_{exp} are
smaller than *Q*_{des} for all nanocavities due to
*Q*_{imp}, according to the following relation:

The reciprocal *Q* values are the optical losses; we use them to discuss the mechanisms by which *Q*_{exp} is reduced. The bars in Fig. 1 show the experimental loss (1/*Q*_{exp}) for each nanocavity, divided into the design loss (1/*Q*_{des}) and the imperfection loss (1/*Q*_{imp}). It can be seen that a reduction of 1/*Q*_{imp} would significantly increase *Q*_{exp} 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/*Q*_{imp} is the sum of the scattering loss (1/*Q*_{scat}) and the absorption loss (1/*Q*_{abs}) as follows:

*Q*

_{abs}.

## 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*: *a*_{2} = *a*_{1} +
*Δa*, *a*_{3} = *a*_{1} +
2*Δa*. We prepared two types of samples with
*Q*_{des} ≈58 million and *Q*_{des}
≈20 million. The cavities were separated from the excitation waveguides by 8 rows of air
holes in the measured samples. The additional *Q* factor
(*Q*_{in}) determined by the coupling to the waveguide was calculated to
be ~1.4 × 10^{8} by the 3D FDTD method, which is included in the above
*Q*_{des} 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
H_{2}O 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 SiO_{x} (x < 2). The SiO_{x} surface layer
is more hydrophilic than Si because the oxygen atom has larger electronegativity.

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 (N_{2}) 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 *Q*_{exp} of the cavity was estimated according to the relation *Q*_{exp} = *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 *Q*_{exp} on the ambient humidity

In order to confirm that absorption loss due to surface water occurs, we investigated the effect on *Q*_{exp} of changing the ambient humidity. We used the nanocavity with *Q*_{des} ≈58 million, a higher value than for the cavities used in our previous studies so that changes in 1/*Q*_{abs} would be more prominent. The parameters of this heterostructure were *a*_{1} = 425 nm, *Δa* = 3 nm, and a resonant wavelength (*λ*_{cav}) 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 *Q*_{exp} of 4.86 million. These were the standard measurement conditions used in our previous reports [6–8]. Second, the chamber was filled with dry N_{2}, reducing the RH to < 5%. We measured the same nanocavity 30 minutes after this air replacement, which resulted in an increase of *Q*_{exp} to 5.09 million. Third, the chamber was filled with humid N_{2}, increasing the RH to 74%. The measurement was carried out using the same procedure, yielding a *Q*_{exp} of 4.48 million. Finally, the chamber was filled again with dry N_{2} and *Q*_{exp} returned to 5.08 million.

Table 1 summarizes these results and Fig. 3 shows the relation between the humidity and
1/*Q*_{imp} calculated using Eq.
(1). It is seen that 1/*Q*_{imp} increases linearly with
humidity. This dependence is most likely caused by the adsorption and desorption of
H_{2}O molecules on the surface. The increase of 1/*Q*_{imp}
between RH values of 5% and 74% is 2.68 × 10^{−8}, corresponding to an
increase of 1/*Q*_{abs}. We quantitatively evaluate this increase as
representing the number of surface H_{2}O molecules adsorbed.

We assume that the H_{2}O 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/*Q*_{abs} can be evaluated from the following equation:

*n*are the absorption coefficient and the refractive index. We used values of

*α*= 6.4 cm

^{−1}and

*n*= 1.31 for liquid H

_{2}O at

*λ*

_{cav}= 1.63 μm [26]. The parameter

*η*is an effective conversion factor based on the surface water volume to cavity volume ratio:

*η*=

*S*×

*T*

_{water}/

*V*

_{cav}, where S is the effective surface area,

*T*

_{water}is the thickness of the H

_{2}O layer, and

*V*

_{cav}is the cavity volume. We approximated the area of nanocavity as the rectangular with dimensions $\sqrt{3}{a}_{1}\times 4{a}_{1}$ 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

*V*

_{cav}were calculated as 9.46 ×

*a*

_{1}

^{2}and 3.59 ×

*a*

_{1}

^{3}, respectively. Under these assumptions, the increase of

*T*

_{water}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 H

_{2}O molecule to be 29.9 Å

^{3}(molar volume /Avogadro constant), the number of H

_{2}O molecules that were newly adsorbed on the cavity surface on increasing the RH was estimated to be 1.95 × 10

^{6}. This value corresponds to 1.14 H

_{2}O molecules per nm

^{2}.

## 5. Drastic increase of *Q*_{exp} by chemical treatment

It is known that once H_{2}O molecules are adsorbed on a SiO_{x} surface, they
are not completely desorbed by decreasing the humidity [27,28]. Therefore, we next investigated the
effect on *Q*_{exp} of applying chemical treatment to remove the thin
SiO_{x} layer at the surface. In this experiment, we used the nanocavity with
*Q*_{des} ≈20 million. The parameters for this heterostructure
were as follows: *a*_{1} = 410 nm, *Δa* = 4 nm, and
λ_{cav} ≈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
*Q*_{exp} in dry N_{2} 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/*Q*_{imp} 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.

After the measurements above, the chip was dipped into dilute hydrofluoric acid (DHF) to remove the thin SiO_{x} layer. It was then rinsed with deionized water and dried by a stream of N_{2}. After this process most of the surface was terminated with hydrogen atoms. Such a surface is known to be more hydrophobic than SiO_{x} 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 N_{2} to prevent H_{2}O 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 *Q*_{exp} occurred for all the measured cavities. We note that *Q*_{exp} decreased almost to the initial values when the chip was left in a standard air environment for a few days. Therefore, this increase of *Q*_{exp} does not originate from a decrease of 1/*Q*_{scat} but rather from a decrease of 1/*Q*_{abs}. 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 *Q*_{exp} 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/*Q*_{abs} values to all the cavities. In other words, the variation in 1/*Q*_{imp}, namely S.D.(1/*Q*_{imp}), can mainly be attributed to fluctuations of 1/*Q*_{scat} 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/*Q*_{scat} for the nine measured cavities and finally derive the absolute value of 1/*Q*_{abs}.

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 *σ*_{hole}. 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/*Q*_{scat} (details of the calculations are given in [18]):

Figure 4(a) shows a contour map of the appearance
frequency of 1/*Q*_{scat} as a function of
*σ*_{hole}, with lines superimposed to represent the above values
of Avg.(1/*Q*_{scat}) and ±
S.D.(1/*Q*_{scat}). Comparison with these simulation results gives
*σ*_{hole} = 0.47 nm and
Avg.(1/*Q*_{scat}) = 1.65 × 10^{−7} for the
measured samples. Therefore, the absolute value of 1/*Q*_{abs} before
chemical treatment was determined as 1.24 × 10^{−7} from Eq. (2). Although
S.D.(1/*Q*_{imp}) 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 *Q*_{exp} before the process.
The value of S.D.(1/*Q*_{imp}) should be the same before and after DHF
treatment because this process does not change the magnitude of
*σ*_{hole}. Therefore, a more realistic estimate of the
1/*Q*_{abs} after the treatment is 0.13 ×
10^{−7}.

Figure 4(b) presents the breakdown of the average (1/*Q*_{exp}) before and after the DHF process. The contribution of 1/*Q*_{abs} to 1/*Q*_{exp} was reduced to 5.7% by removing the SiO_{x} layer. Using Eq. (3), the reduction in *T*_{water} was 9.79 × 10^{−2} nm where α = 9.4 cm^{−1} at 1570 nm [26]. If 1/*Q*_{abs} is completely attributed to the surface water, it can be concluded that 4.24 H_{2}O molecules/nm^{2}, corresponding to *Q*_{abs} 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 H_{2}O molecule of 0.125 nm^{2} in the Brunauer–Emmett–Teller (BET) theory [29], it is estimated that 53% of the surface is covered by H_{2}O molecules. This estimation almost agrees with that obtained by mass measurement (80% coverage) for a natural SiO_{2}/Si(100) surface [28]. Therefore, we suspect that the adsorption of surface water represents the main contribution to 1/*Q*_{abs} 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 *T*_{water} have some uncertainty.) It is also possible that absorption by interface states between the Si and SiO_{x} plays a role [31]. Measurements using a dry O_{2} 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
*Q*_{exp} of 9.05 million, which is 2.3 times larger than the previous
record value. Here, we used the nanocavities with *Q*_{des} ≈20
million, which were of lower quality than those measured in our previous work [8]. We thus believe that a *Q*_{exp}
exceeding 10 million will be obtained in the near future using nanocavities with improved
*Q*_{des} and fabrication accuracy.

## 7. Summary

We have investigated the optical loss that results from surface water adsorbed on Si heterostructure nanocavity samples. We have shown that the *Q*_{exp} 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 SiO_{x} layer at the surface. As a result, we have achieved a *Q*_{exp} 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 *Q*_{abs} factor about 7 million exists in standard Si high-*Q* nanocavities. These results represent great steps toward a *Q*_{exp} 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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