Photonic crystal nanocavities that simultaneously possess small modal volumes and high quality (Q) factors have opened up novel research areas in photonics during this decade. Here, we present an important key for the increase of Q factors to ranges beyond ten million. A systematic investigation on photon lifetimes of air-bridge-type heterostructure nanocavities fabricated from silicon on insulator (SOI) substrates indicated the importance of cleaning the bottom side (buried oxide side) of the nanaocavites. Repeated thermal oxidation and an oxide removal process applied after the removal of the buried oxide layer underneath the nanocavities realized an experimental Q factor greater than eleven million, which is the highest experimental Q ever recorded. The results provide important information not only for Si PC nanocavities but also for general Si nanophotonic devices and photonic electronic convergence systems.
© 2017 Optical Society of America
Photonic nanocavities based on artificial defects in two-dimensional (2D) photonic crystal (PC) slabs [1–3] have recently realized extremely high quality (Q) factors in the range of tens of thousands to millions or more together with small modal volumes (V) of the order of one cubic wavelength or less. Because such photonic nanocavities can concentrate electromagnetic energy in both space and frequency domains, they are one of the most important tools to manipulate photons, and are widely used in various scientific and engineering fields. There have been various efforts to increase the Q factors of 2D-PC slab nanocavities both in theory and experiment [4–17]. Methods to maximize of Q/V [18–21] and those to obtain high Q factors without using air-bridge structures [22–24] have been also intensively studied.
Meanwhile, the realization of nanocavities with Q factors greater than thousands leads to development of low threshold nanolasers [19, 20, 25, 26] which can be used for high-performance material sensing. The development of nanocavities with Q factors greater than tens of thousands  realized strongly coupled light-matter systems in solid [27–29], a few and single quantum dot(s) lasers [30, 31], quantum-logic gates , on-demand catch/release of photons , etc. Furthermore, nanocavities with Q factors greater than hundreds of thousands enabled exotic photon manipulation technologies including ultra-low threshold InP-b/InGaAsP  and Si Raman  lasers, ultra-low-power consumption optical bistable systems , strong coupling of distant nanocavities  with adiabatic photon transfer , and the like. Further improvement of the Q factors will improve the performances of these techniques and also open up new frontiers in photon manipulation.
So far, the highest experimental Q factors (Qexp) have been obtained in heterostructure-type Si slab nanocavities made from silicon-on-insulator (SOI) wafers [5, 6, 8–13, 15]. In general, Qexp is determined by design, structural fluctuations, and optical absorptions, where the last factor is most difficult to investigate. In this connection, we recently reported that a remarkable increase of Qexp was observed after dipping the nanocavities in dilute HF (DHF) to remove a thin oxide layer naturally formed on the Si surface; the best nanocavity showed a record Qexp of nine million . However, the average Qexp obtained in that study was 4.4 million for six measured nanocavities , which is quite low compared to the highest Qexp of nine million; the variance seems to be attributable to the instability of the natural oxidization process that depends on many complex parameters including humidity, temperature, storage time, and contamination.
In this paper, we present a systematic investigation of Qexp of Si heterostructure-type nanocavities during several repetitions of controlled surface oxidization and oxide removal treatments. We show that it is important to clean the bottom side (buried oxide side) of the nanaocavites. This process stably reproduced an average Qexp over 7.5 million, and realized the record highest Qexp exceeding eleven million. These studies will provide important information not only for Si PC nanocavities but also for general Si nanophotonic devices and photonic electronic convergence systems.
2. Sample structure and experimental setup
Figure 1(a) shows a schematic of the 2D-PC slab 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, where the base lattice constant a1 is 410 nm. The nanocavity was formed by a line defect of 17 missing air holes where the lattice constant in the x-direction was increased from the center to outer every two periods by 3 nm twice as shown in Fig. 1(a). In addition, the blue air holes in Fig. 1(a) were shifted by 0.001a1 outward in the y-direction, and the red air holes were shifted by 0.002a1 outward in the x-direction; a leaky component visualization method  was used for the optimization of the design. The design Q factor (Qdes) and the modal volume were calculated by the three-dimensional finite-difference time-domain (3D-FDTD) method to be 1.3 × 108 and 1.4 cubic resonant wavelengths in the material. An excitation waveguide which was 10%-wider than the cavity was prepared in parallel with the cavity, where the distance between them was six rows of air holes. The additional Q factor determined by the in-plane coupling to the excitation waveguide (Qin) was calculated to be ~6 × 107 by the 3D FDTD method. Therefore, the actual Qdes was calculated to be 4 × 107 by including the load of Qin.
The samples were fabricated on a SOI substrate prepared by Soitec using the Smart Cut method. The thickness of the top Si slab is 220 nm and that of the buried oxide (SiO2) is 3000 nm. The top Si is doped with boron and its resistivity is 10 Ωcm, from which the doping density is estimated to be of the order of 1 × 1015 cm−3. After defining the PC pattern by using electron beam lithography on the resist mask coated on the wafer, the pattern was transferred to the top Si slab by an inductively coupled plasma etching process using SF6-based gas. The sample surface was cleaned by standard cleaning process for Si wafers, and by thin thermal oxidation with a subsequent removal of the surface oxide. The PC area was 300 μm × 15 μm, and nine nanocavities were placed along the excitation waveguide with a period of 20 μm, similar to those used in the previous reports . One side of the waveguide end was cleaved to form an input facet for excitation light. We labeled the nanocavities as #1, #2, ..., #9 in ascending order of distance from the input facet. Finally, the buried oxide underneath the PC slab was removed by HF to form an air-bridge structure.
Figure 1(b) shows the measurement system used. Several modifications have been made from the previous study  in order to enable controlled oxidization. Samples were put on a sample stage equipped with a heater and thermocouple for oxidization at elevated temperatures up to 300°C. They were placed in an isolation chamber in which the ambient can be controlled by using dry inert gas (N2 or Ar) or dry air. Excitation light was introduced in the chamber through an optical fiber of which end facet was shaped into a lens. The position of the optical fiber was aligned by a xyz-stage driven by actuators. We performed time-domain measurements as outlined in Fig. 1(b) to evaluate the lifetimes (τ) of photons trapped in the nanocavities: We excited a cavity by an optical pulse with a duration of 10 ns and measured the decay of photon emission from the cavity by the time-correlated single photon counting method. We evaluated τ from the later part of the decay curve in order to avoid influence of the tail of the excitation pulse (see Fig. 2). The Qexp of the nanocavity was estimated according to the relation Qexp = ωτ, where ω is the resonant frequency. Details of the measurement have been described previously . It is noteworthy that samples were always kept in a dry ambient, except for the processes that required chamber opening (for example, the DHF treatment described below). The chamber wall and sample stage were baked at 80°C and 300°C, respectively, in vacuum for more than one week, before starting the measurement.
3. Experimental results
The experiment was carried out as follows: After the fabrication of a sample with a final dipping into HF to remove the buried oxide, the sample was placed in the measurement chamber filled with a dry inert gas (N2 or Ar), and Qexp values of the nanocavities were measured. Next, the sample was oxidized within the measurement chamber in dry air ambient at an elevated temperature. Qexp values of the nanocavities were evaluated after the sample had cooled down to room temperature. The sample was taken out from the measurement chamber, dipped into DHF, rinsed with de-ionized water, and dried by blowing with dry N2. The sample was returned to the chamber within 15 min after the DHF process and Qexp values were evaluated in dry inert gas ambient. This procedure was repeated four times to check the stability.
Figure 2 shows the photon lifetime curve of one of the prepared nanocavities (#6) just after fabrication, that after the first oxidization process, and that after the first DHF process. It is seen in the figure that τ decreased from 5.2 ns to 3.9 ns after the oxidization and increased to 6.2 ns after the DHF treatment. The corresponding Qexp values are 6.3, 4.7, and 7.5 million, respectively. Simultaneously, the resonant wavelength changed from 1567.5 nm to 1567.26 nm and 1565.30 nm for each treatment step. The blue shifts of the resonant wavelength are caused by the decrease of the refractive index by surface oxidization, and the decrease of the slab volume by oxide removal. The total blue shift of the resonant wavelength (2.2 nm) observed for this process corresponds to the uniform removal of silicon at the cavity surface (including inner walls of the air holes) by about 0.5 nm according to the 3D-FDTD calculation. The decrease of τ after the oxidization is due to the formation of interface states at the Si/SiO2 interface , and the increase of τ after oxide removal is attributed to the removal of the interface states and termination of the Si surface with hydrogen [15, 40–42]. More importantly, one cycle of this treatment increased τ or Qexp by 19%, which demonstrates the effectiveness of this cleaning method. The changes of Qexp and the resonant wavelength of nanocavity #6 through the four repetitions of the above procedure are presented in Table 1. (Here, the maximum Qexp measured after the process is shown, but, in fact, Qexp slowly changes over a few days.) It is seen in the table that Qexp started from 6.3 million, reached to 9.1 million after the second oxidization /DHF treatment, and kept almost 9 million for the subsequent repetition of oxidization /DHF treatments.
We can discuss the reason for the increase of Qexp from several features seen in Table 1: (A) Qexp after the first oxidization (4.7 million) is different from than those after the second, third, and fourth oxidizations (3.6 ~3.9 million). (B) Qexp after the first oxidization/DHF treatment (7.5 million) is less than those after the second ~fourth oxidization/DHF treatments (~9 million). (C) The blue shift of the resonant wavelength after the first oxidization (0.25 nm) is much less than those for the second ~fourth oxidizations (0.9~1.1 nm). These features clearly indicates the situation in the first oxidization/DHF treatment is different from that in the subsequent oxidization/DHF treatments. We suspect influence of the bottom side (buried oxide side) surface of the Si slab: The state of the bottom side surface just after the fabrication is considered to be different from those for the top surface and the inner walls of the air holes because the latter two surfaces already experienced the cleaning processes that includes thermal oxidization and oxide removal during the fabrication while the bottom side surface was always covered with buried oxide that was not removed until the final step of the fabrication. The interface between the top Si and buried oxide can concentrate contamination [43–45], which can remain after the removal of the buried oxide by HF. It is considered that the oxidization/DHF treatment applied after the removal of buried oxide reduced contaminants at the bottom side surface of the nanocavity and drastically improved Qexp.
Table 2 represents Qexp of the 9 prepared nanocavities measured 2 days after the second oxidization/DHF and 5 days after the fourth oxidization/DHF process. It is noted that the controlled oxidization and oxide removal process can consistently reproduce very high Qexp. High Qexp values greater than 6 million were obtained for 8 of the nanocavities in both measurements, and an extremely high average Qexp > 7.5 million is obtained. (We could not determine the resonance of nanocavity #2.) This average Qexp is 60% larger than the previous value of 4.4 million . The relatively smaller Qexp observed after the fourth process is probably due to the longer storage time after the DHF process or fluctuations in the oxidization/DHF process.
Figure 3 shows the longest photon lifetime curves that were obtained for nanocavity #8 just after the fourth oxidization/DHF processes. It can be seen in the figure that a very long photon lifetime of 9.2 ns, which corresponds to a Q factor of 11 million (1.11 × 107), is obtained experimentally. This is a record-breaking Q factor—the highest ever reported for 2D-PC nanocavities. The decay rate did not change for the estimated input power range used here, which indicates that nonlinear effects—especially two-photon absorption—are negligibly small. The Q factor decreased to 9.9 million five days after this measurement (as shown in Table 2) even though the sample was kept in a dry inert gas (N2) ambient.
As we reported before, insights into the origin of the loss due to the imperfections (1/Qimp) can be obtained from the statistical analysis of Qexp . For this analysis, we first remove the loss determined by the design (Qdes) by using the following relation :Table 2. Here, 1/Qimp can be divided into scattering loss (1/Qscat) and absorption loss (1/Qabs) as follows:13]. We performed the calculation for 30 different fluctuation patterns to obtain the statistical relationship between σhole (in nm) and Avg. (1/Qscat), and σhole and S.D. (1/Qscat) as follows :Table 2 using Eq. (4). (Such small fluctuations in positions and radii of air holes are beyoud the observation accuracy of scanning electron microscopes.) When we put σhole = 0.25 nm into Eq. (3), experimental Avg.(1/Qscat) is estimated to be 4.7 × 10−8, and therefore experimental Avg.(1/Qabs) is estimated to be ~5.8 × 10−8 using experimentally obtained Avg.(1/Qimp) of 1.05 × 10−7 and Eq. (2). As a result, the ratio of the average contribution of 1/Qdes, 1/Qscat, and 1/Qabs to 1/Qexp are estimated to be about 20%, 35%, and 45%, respectively. We think there is still room for improvement of Qexp because the contribution of the design on the total loss is only 20%, but for that purpose, the origin of the absorption loss should be clarified. Possible origins are free-carriers supplied from surface stastes or residual impurities of the silicon slab.
Incidentally, Avg.(1/Qabs) of 5.8 × 10−8 for the eight samples after the fourth controlled oxidization/DHF treatment is larger than Avg.(1/Qabs) of 1.3 × 10−8 that we previously reported for the six samples with one application of natural oxidization/DHF treatment . This is because we underestimated the value in the previous study due to the assumption that the fluctuation of 1/Qabs should be negligible. As opposed to this assumption, the instability of the natural oxidization process could have caused the fluctuation of 1/Qabs. As a result, we overestimated S.D.(1/Qscat) and σhole, which led to the evaluation of larger Avg.(1/Qscat) and smaller Avg. (1/Qabs). The instability can be also the origin for the smaller average Qexp of 4.4 million, compared to the highest Qexp of nine million, in the previous study .
We have successfully improved the experimental Q factors of air-bridge type Si-based 2D-PC nanocavities from the order of 4.4 million to over 7.5 million on average by cleaning the air-bridge structure using controlled dry oxidization and subsequent oxide removal by dilute HF. A record-high Q factor of 11 million was obtained immediately after the fourth cycle of this cleaning process. It is considered that the improvement of the bottom side (buried oxide side) of the Si slab accounts for this drastic improvement of Q factors. The fluctuations of radii and positions of air holes after this cleaning process have been evaluated to be < 0.25 nm by a statistical investigation. The contribution of design, scattering, and absorption to the experimental Q factors of the nanocavities is approximately 20%, 35%, and 45%, respectively. We believe that the high-Q nanocavities obtained in this report will stimulate various scientific and engineering fields.
JSPS KAKENHI (23360033 and 15H05428); New Energy and Industrial Technology Development Organization (NEDO).
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