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The photonic band diagrams of the photonic crystal slabs (PCSs) with various structural air holes were calculated by plane wave expansion method with super cell method. The calculated results indicate that the PCSs with hexagonal or triangular air holes have enough large photonic band gaps in the guided mode spectrum, hence they are good candidates to be used for the PC devices. The PCs with hexagonal or triangular air holes were fabricated successfully on n-type GaAs (111)B substrate by selective-area metal organic vapor phase epitaxy (SA-MOVPE). Vertical and smooth facets are formed and the uniformities are very good. The same process was also used to fabricate hexagonal air hole arrays with the width of 100 nm successfully. A procedure was proposed and utilized to fabricate the air-bridge PCS with normal hexagonal air holes. The fabricated hexagonal air holes are very uniform and the sidewalls are smooth and vertical. Our experimental results indicate that SA-MOVPE growth is a promising low-damage fabrication method for PC devices and photonic nano-strucutres.
©2005 Optical Society of America
Introduction
Since the pioneering work of E. Yablonovitch and S. John [1, 2], photonic crystals (PCs), artificial optical materials with periodically modulated refractive indices, have attracted much attention. Due to the existence of photonic band gaps (PBGs), in which the propagation of the electromagnetic wave with specific frequency is forbidden, PCs are considered as potential materials for controlling spontaneous radiation and light guiding. Compared with three-dimensional PCs, PC slab (PCS) only has PBGs in the x-y plane and uses index difference to confine the optical field in the z direction, thus it can be fabricated more easily by using established semiconductor processing technology.
Although great improvements have been achieved since the first suggestion of the concept of PCs, there is still a long way to go before their actual application. For example, the lowest reported propagation loss for silicon on insulator (SOI) PC waveguides is 0.6 dB/mm [3], which is two orders of magnitude larger than that of the conventional SOI waveguides [4, 5]. The lowest reported propagation loss for GaAs PC waveguides is 0.76 dB/mm [6], which is still one order of magnitude larger than that of the conventional GaAs waveguides [7]. The pulsed lasing of the PC microlaser at the low temperature and optical pumping was first reported by O. Painter at 1999 and its continuous lasing at the room temperature and optical pumping was also reported [8, 9]. Recently, electrically driven pulsed lasing at the room temperature has been reported by H. G. Park [10]. However, there are still no reports on its electrically driven continuous lasing at the room temperature. Most of the reported PC devices were fabricated by dry etching method. Therefore process-induced damage and relatively rough air-dielectric interfaces, which greatly increase the propagation loss of PC waveguides and the threshold current of laser diodes, are unavoidable.
One way to overcome this drawback is to further optimize the dry etching process. Another way is to try other intrinsically low-damage fabrication methods such as wet etching and/or selective area epitaxy [11, 12]. However, the shapes of the holes or pillars fabricated by these two methods depend not only on the pattern formed on the material surface but also on the orientation of the crystal plane. Fortunately, most semiconductor materials have diamond, zinc blende or wurtzite crystal structures. For these materials, if the (111) plane is used as the substrate and {11¯0} planes are used as the sidewalls, hexagonal or triangular air holes or dielectric pillars can be formed. Actually, selective area metal organic vapor phase epitaxy (SA-MOVPE) has been used successfully to fabricate several types of uniform hexagonal semiconductor pillar arrays on GaAs (111)B or InP (111)A and B substrates [13~16]. However, the shapes of the hexagonal air holes fabricated by this method deform from the designed structures and become irregular due to the overgrowth at the six corners along < 21¯1¯> and <2¯11> directions [17, 18].
In this paper, we will report the new development on the fabrication of the PCs with hexagonal or triangular air holes by SA-MOVPE. The photonic band diagrams of the PCSs with hexagonal or triangular air holes were calculated by plane wave expansion method (PWE) with the super cell method [19–23]. It is found that the PCSs with hexagonal air holes or triangular air holes have enough large PBGs in the guided mode spectrum, thus they are good candidates to be used for PC devices. By optimizing the lift-off process and the growth conditions such as growth temperature and the partial pressures of trimethylgallium (TMG) and arsine (AsH3), we have successfully fabricated the PCs with hexagonal or triangular air holes. A procedure was proposed and utilized to fabricate the air-bridge PCSs with normal hexagonal air holes. The fabricated air holes are hexagonal, uniform and have smooth and vertical sidewalls.
2. Calculation results and discussion
The triangular lattice was selected as the studied object because it has larger PBGs than square and hexagonal lattices. The refractive index of the studied semiconductor material is 3.374 (n GaAs=3.374 at 1.55 μm). Both the top and bottom claddings are air (n air=1). These structures correspond to the air-bridge PCSs, which supply the strongest confinement in the vertical direction to the optical field and are most likely to be used for PC devices. The slab thickness (t) was selected to be 0.6a for the PCSs with various structural air holes so that they have relatively larger PBGs in the guided mode spectrum, where a is the lattice constant. The PWE method with the super cell method was used to calculate the photonic band diagrams of the PCSs with various structural air holes [19–23]. The supercell is 6a in the vertical direction, which is thick enough to prevent the coupling of the optical fields in the neighboring supercells. The grid point number (Na×Nb×Nc, where Na, Nb and Nc are the grid point numbers along the lattice vectors a and b and the vertical vector c) used in the calculation is 16×16×128, which is sufficient to give a relatively accurate result in a reasonable computation time.
It is well known that the modes of the PCSs can be classified into leaky and guided modes. The former are continuous quasi-eigenmodes with finite lifetimes and have effective indices less than those of the top and bottom claddings. Thus a “light line” filter was used to remove these states from the calculated photonic band diagrams. The latter are discrete genuine eigenmodes with infinite lifetimes and have effective indices larger than those of the top and bottom claddings. Therefore, they are only located in the region of the photonic band diagram that is under the “light line”. “PBG in the guided mode spectrum” was adopted to indicate such a region in the photonic band diagram, where there are no guided modes, and “photonic gap map in the guided mode spectrum” to indicate such a figure, in which PBGs for only guided modes are plotted as a function of the structural parameters.
Because of the reduced symmetry compared with circular air holes, there are numerous arrangements for hexagonal, triangular and square air holes with respect to the triangular lattice. However, here we only consider two specific arrangements for hexagonal and triangular air holes, which are most likely to be used for PC devices, and one specific arrangement for square air holes since it is almost impossible to fabricate this structure by SA-MOVPE. Depending upon whether one side of the hexagon is perpendicular or parallel to the Γ-K direction, the structure will be termed the normal or orthogonal hexagonal air holes (as shown in the insets of figs. 1(b) and 1(c)), respectively. Depending upon whether one side of the triangle is parallel or perpendicular to the Γ-K direction, the structure will be termed normal or orthogonal triangular air holes (as shown in the insets of figs. 1(e) and 1(f)), respectively.
Fig. 1. Photonic gap maps in the guided mode spectrum for the PCSs with circular air holes (a), normal hexagonal air holes (b), orthogonal hexagonal air holes (c), square air holes (d), normal triangular air holes (e) and orthogonal triangular air holes (f). TE-like modes are shown in solid lines “—” and TM-like modes in dotted lines “…”.
Figures 1(a)~1(f) show the photonic gap maps in the guided mode spectrum of the PCSs with various structural air holes. For the PCSs with circular, hexagonal or square air holes, there are five PBGs in the guided mode spectrum, three of which are for TE-like modes (as shown in solid lines) and the other two for TM-like modes (as shown in dotted lines). Furthermore, these PBGs in the guided mode spectrum are very similar and obviously larger than those of the PCSs with triangular air holes (also as shown in figs. 2(b) and 2(d)). Thus it is better to select the PCSs with circular, hexagonal or square air holes for the PC devices requiring large working bandwidth. In some cases, if we do not care too much about the working bandwidth, the PCSs with triangular air holes also can be used for PC devices. Due to the much lower filling fraction of the air for the PCSs with triangular air holes, their guided mode spectra shift to the lower frequency compared with those of the PCSs with circular, hexagonal and square air holes and thus there are more PBGs in the guided mode spectrum in the same frequency range. When we overlap all the first PBGs in the guided mode spectrum for TE-like modes of the PCSs with various structural air holes, we find that the frequency positions of their first PBGs in the guided mode spectrum (F) for the same r/a values satisfy the following relation: Ftrianguiar < Fcircuhr < Fhexagonal < Fsquare (also as shown in fig. 2(a)). This behavior can be explained as follows. Based on the electromagnetic variational theorem [21], a mode tends to concentrate its displacement energy in high-index region, while remaining orthogonal to the mode below it in frequency. It should be noted that the definition for r is different for different types of PCSs. For example, r is the radius for circular air holes, half the distance between two opposite sides for hexagonal air holes and half the side length for square and triangular air holes. The areas of these structural air holes (A) satisfy the following relation: Atrianguiar < Acircuiar < Ahexagonai < Asquare. Since the slab thickness was selected to be the same value (0.6a) for the PCSs with various structural air holes, the volumes of these structural air holes (V) satisfy the following relation: Vtrianguiar < Vcircuiar < Vhexagonai < Vsquare. Thus the optical fields penetrating into the various structural air holes (P) satisfy the following relation: Ptrianguiar < Pcircuiar < Phexagonai < Psquare, which leads to the shift of the first PBG in the guided mode spectrum to the higher frequency from the case of the PCS with triangular air holes to the case of the PCS with square air holes. If the first PBG in the guided mode spectrum was plotted as a function of the filling fraction of the air holes, we can see that all the first PBGs in the guided mode spectrum are almost located at the same positions (also as shown in fig. 2(c)), which indicate that the frequency position of the first PBG in the guided mode spectrum is mainly dependent on the filling fraction of the air holes and independent on the structure of the air holes. However, the width and the structure of the first PBG in the guided mode spectrum is not only dependent on the structure of the air holes but also on the filling fraction of the air holes (also as shown in figs. 2(b) and 2(d)).
Fig. 2. Gap-mid and gap-ratio as the functions of the normalized sizes and filling fractions of the air holes. Solid square “■”is for the PCS with circular air holes, hollow square “□” for the PCS with normal hexagonal air holes, solid circle “●”for the PCS with orthogonal hexagonal air holes, Hollow circle “○” for the PCS with square air holes, solid triangle “▲” for the PCS with normal triangular air holes and hollow triangle “△” for the PCS with orthogonal triangular air holes.
We also find that the PBGs in the guided mode spectrum of the PCSs with air holes shift to the higher frequency with increasing the size of the air holes. This phenomenon also can be explained on the basis of the electromagnetic variational theorem [21]. For the PCSs with air holes, the optical field penetrating into the air holes increases with an increase in the size of the air holes, which increases the energies of the guided modes and the PBGs in the guided mode spectrum. It should be noted that there are some PBGs in the guided mode spectrum for both TE-like modes and TM-like modes for all the PCSs considered here. However, these full PBGs are located at a little higher frequency range, which maybe affects their actual application due to the limit available k-space and the low durability to structural errors.
3. Experimental results
Due to the structural symmetry of GaAs material, if (111)B facet is used as the substrate, there are six vertical {1¯10} facets, which gives rise to the possible formation of hexagonal air holes. Furthermore, if the growth on some facets is prohibited purposivly, other structures such as triangular air holes are possibly formed. SA-MOVPE is thought to be the most promising method to realize such structures because in this method faceting technology can be used and process-induced damages and contamination can be avoided. Firstly, we’d like to discuss the possibility of the formation of the hexagonal or triangular air holes directly on the n-type GaAs (111)B substrate. The fabrication procedure started with the spin-coating of ZEP520 resist on the n-type GaAs (111)B substrate and the designed pattern was formed on it by electron beam (EB) lithography. Then about 30 nm thick SiO2 layer was deposited by plasma sputtering and the pattern formed on the resist was transferred onto the SiO2 layer by the lift-off process. Finally, about 200 nm thick GaAs layer was grown on the exposed region of the n-type GaAs (111)B substrate by SA-MOVPE.
Fig. 3. SEM images for the patterned substrates of the PCs with normal hexagonal air holes (a), orthogonal hexagonal air holes (b), normal triangular air holes (c) and orthogonal triangular air holes (d).
For the growth of semiconductor pillars, hexagonal pillars can be formed even the masked pattern becomes circular due to the limit resolution of EB lithography and wet etching [13~16]. This self-healing growth mode facilitates the growth of semiconductor hexagonal pillars. However, there is not such a self-healing characteristics in the growth of hexagonal or triangular air holes, so we should optimize the fabrication process of the masked pattern for their growth very carefully. On the other hand, the residual resist will pollute the reactor chamber and affect the crystal quality of the GaAs epitaxial layer. In order to achieve high-quality patterned substrates, several steps should be controlled very carefully. Firstly, the thickness of ZEP520 resist was kept stable by controlling the rotation speed of the spin-coater. Then appropriately thick SiO2 layer was deposited on the n-type GaAs (111)B substrate and the samples were dipped into the 1165 remover for 2 days. Finally, the 1165 remover was baked at about 100 °C for 1 hour and the samples were ultrasonically cleaned in turn in 1165 remover for 5 mins, MEK solution for 5 mins and acetone for 5 mins in order that the resist and the SiO2 on it could be removed completely. Figures 3(a)~3(d) show the scanning electron microscope (SEM) images of the patterned n-type GaAs (111)B substrates after the lift-off process. The lattice constant was selected to be 500 nm and 800 nm for the hexagonal and triangular air hole arrays, respectively, and the normalized size (r/a) of the air holes was selected to be 0.3 in all cases so that the fabricated PCs can work at the optical communication wavelength (1.55 μm). It can be seen that resist and the SiO2 on it are removed completely and uniform hexagonal or triangular SiO2 masked patterns are formed, which supplies the premise and base for the growth of high-quality hexagonal or triangular air holes.
Fig. 4. SEM images for the fabricated PCs with normal hexagonal air holes (a), orthogonal hexagonal air holes (b), normal triangular air holes (c) and orthogonal triangular air holes (d).
The subsequent growth was carried out in a horizontal low-pressure MOVPE system. The source materials were TMG and 5% AsH3 in hydrogen. The working pressure was fixed at 76 Torr. Patterned substrates were heated from the room temperature to a thermal cleaning temperature of 650 °C for five minutes and then fixed at a growth temperature. It is known that the epitaxial growth rate is dependent on the crystallographic orientation. For example, the GaAs (111)B facet tends to grow under higher growth temperature and lower AsH3 partial pressure, while the GaAs {11¯0} facets tend to grow under lower growth temperature and higher AsH3 partial pressure. In order to prevent the lateral growth in the <11¯0> directions and enhance the growth rate in [111] direction, the growth temperature and the partial pressure of AsH3 were selected to be 800 °C and 1.3×10-5 atm. The partial pressure of TMG was selected to be 1.3×10-6 atm. In such a growth condition, the growth rate is very low (about 1.8 nm/min), which is very important for the formation of the facets. Figures 4(a)~4(d) show the SEM images for the fabricated PCs with hexagonal or triangular air holes. From these figures, we can see that the PCs with hexagonal or triangular air holes have been fabricated successfully. The uniformities of the fabricated PCs are very good. The formation of the hexagonal or triangular air holes also indicates that facets are formed. When we compared the SEM images in fig. 4 with those in fig. 3, we can see that the patterns in fig. 3 are replicated completely in fig. 4, which indicate that the sidewalls of the air holes are vertical.
Fig. 5. (a) SEM image for the cross section of the fabricated PC with normal hexagonal air holes. (a) SEM image for the fabricated PC with normal hexagonal air holes. (b) and (c) SEM images for the fabricated PC waveguide with normal hexagonal air holes and the fabricated PC microcavity with normal hexagonal air holes. (d) SEM image for the fabricated PC with normal hexagonal air holes and a=200 nm and r=50 nm.
In order to testify this, we selected the fabricated PC with normal hexagonal air holes as the studied object and cleaved it cross the patterned region and observed its cross section by SEM. Figure 5(a) shows the SEM image for its cross section. We find that the sidewalls are vertical (almost 90 °). Figure 5(b) shows the high-resolution SEM for the fabricated PC with normal hexagonal air holes and a=300 nm and r/a=0.3. We can see that the surface and the sidewalls are very smooth. The maximum roughness should be less than 5 nm. The characteristics of the air holes is important for actual application because inclined air holes will enhance the coupling of TE-like waveguide modes and TM-like slab modes and thus increase the propagation loss of the PC waveguides [24], and the rough surface and sidewalls will enhance the surface recombination and thus increase the threshold current of PC laser diodes. Figure 5(c) shows the SEM image for a line-defect PC waveguide with normal hexagonal air holes. We can see that the interface between the air and the line-defect region is very smooth, which indicates that the propagation loss of the PC waveguide device fabricated by this method can be reduced greatly since smooth interface can reduce the scattering loss. Theoretical calculation indicates that by adjusting the width of the line defect and the size of the hexagonal air holes along the line defect, a guided mode with a bandwidth as high as 9.1% of its central frequency can be reached [20]. Our experimental results together with the related theoretical calculations indicate that SA-MOVPE growth can be used to fabricate the PC waveguide devices with low propagation loss and large bandwidth and thus can be used to fabricate complex PC integrated optical circuits. Figure 5(d) shows the SEM image for a PC microcavity with normal hexagonal air holes. The sidewalls are very smooth, which can reduce the surface recombination greatly, thus decrease the threshold current of PC laser diodes fabricated by this method.
In the above, we have discussed the fabrication of the PCs with hexagonal or triangular air holes working in the optical communication wavelength by SA-MOVPE. However, sometimes we also need to fabricate the PCs with hexagonal or triangular air holes working at shorter wavelengths. In order to testify whether our fabrication process can be used for such structures, we designed one PC pattern with the period of 200 nm and the width of the hexagonal air holes being 100 nm. Figure 5(e) shows the SEM image for such a structure. We can see that hexagonal air holes with vertical and smooth facets are formed and their uniformities are very good. We think that hexagonal air holes with the width less than 100 nm can also be fabricated using the above fabrication process.
Fig. 6. SEM images for the fabricated air-bridge PCS with hexagonal air holes (a=300 nm and r=90 nm) (a) and its cross section (b).
As discussed in the above, uniform hexagonal or triangular air holes with vertical and smooth sidewalls can be fabricated successfully on the n-type GaAs (111)B substrate by SA-MOVPE. However, in such structures, due to the short of the index difference between the core region and the GaAs substrate, the PC slab modes are located above the light-line of the GaAs substrate, thus large radiation loss to the substrate is unavoidable. For the actual application of the above fabrication process for the PC devices, the confinement to the optical field in the vertical direction should be introduced. To achieve this aim, a sacrificial layer needs to be found, which can be used as the substrate for the high-quality growth of GaAs epitaxial layer and selectively etched without damaging the formed GaAs PC patterns. AlGaAs is the most appropriate material for such a purpose. A proposed fabrication procedure for the air-bridge PCSs with hexagonal or triangular air holes is shown here. It started with an epitaxial growth of GaAs buffer layer, Al0.5Ga0.5As sacrificial layer and GaAs cap layer on GaAs (111)B substrate. Next, ZEP520 resist was spin-coated on the epitaxially grown GaAs cap layer and the designed pattern was formed on it by EB lithography and selective etching of GaAs cap layer. Then about 30 nm thick SiO2 was deposited by plasma sputtering and the pattern formed on the resist was transferred onto the SiO2 layer by the lift-off process. After the formation of the SiO2 mask, about 200 nm thick GaAs layer was grown on the exposed region by SA-MOVPE. Finally, the remained SiO2 and the underlying Al0.5Ga0.5As layer were selectively etched by hydrofluoric acid solution to form the air-bridge structure. Compared to the growth directly on the GaAs (111)B substrate, there are another two technological challenges for the fabrication of the air-bridge PCSs. The first one is about the growth of Al0.5Ga0.5As sacrificial layer. In order to grow high-quality Al0.5Ga0.5As sacrificial layer, the growth temperature was set to be 850 °C. The partial pressure is 1.3×10-5 Torr for AsH3, 3.2×10-6 Torr for TMG and 1.2×10-6 Torr for TMA. It should be pointed out that there are some bubbles in the sacrificial layer and further optimization to the growth condition for Al0.5Ga0.5As is still needed. The second one is about the selective etching process of GaAs cap layer. H3PO4:H2O2:H2O=1.5:0.5:37.5 was used as the solution for the selective etching of GaAs cap layer. Figure 6(a) shows the SEM image for the fabricated air-bridge PCSs with hexagonal air holes and a=300 nm and r=90 nm. It can be seen that the same uniform hexagonal air holes as the PCs grown directly on the GaAs (111)B substrate are formed. Figure 6(b) shows the SEM image for the cross section of the fabricated air-bridge PCSs. We find that vertical and smooth sidewalls are formed. We also find that the undercut cladding GaAs is not perforated completely, which can be removed entirely by increasing the selective etching time.
4. Conclusion
In summary, we have calculated the photonic band diagrams of the PCSs with various structural air holes using PWE method with the super cell method and find that the PCSs with hexagonal air holes have PBGs in the guided mode spectrum that can be compared to that of the PCS with circular air holes, hence they are also good candidates to be used for the PC devices. In some cases, if we do not care too much about the working bandwidth, the PCSs with triangular air holes also can be used for PC devices. The PCs with hexagonal or triangular air holes were fabricated successfully on n-type GaAs (111)B substrate by SA-MOVPE. Vertical and smooth sidewalls are obtained and the uniformities are very good. The same process was also used to fabricate hexagonal air hole arrays with the width of 100 nm successfully. The air-bridge PCS with normal hexagonal air holes and a=300 nm and r=90 nm was also fabricated successfully by SA-MOVPE. The hexagonal air holes are very uniform and the sidewalls are very smooth and vertical. Further optimization of the growth condition for the sacrificial layer and the selective etching process of GaAs cap layer is needed. Generally, process-induced damages to the active regions can be avoided in SA-MOVPE only if high-quality masked pattern is fabricated successfully, which is unavoidable in the usually used dry etching method. However, the growth of high-quality reactive region, for example, InGaAs/GaAs quantum well on GaAs (111)B substrate is not easy as there are very few reported results on the growth of InGaAs/GaAs quantum well on GaAs (111)B substrate by MOVPE. Recently, we have succeeded in growing high-quality pillars with InGaAs/GaAs quantum well on GaAs (111)B substrate and observed strong photoluminescence at about 1 μm from these samples, which maybe helps us to optimize the growth condition of the air holes with InGaAs/GaAs quantum well on GaAs (111)B substrate. In conclusion, our experimental results indicate that SA-MOVPE growth is a promising low-damage fabrication method for PC devices and photonic nano-structures.
Acknowledgments
The authors thank Mr. Akamatsu for technical support in MOVPE growth. This work is partly financially supported by a Grant-in-Aid for Scientific Research and is also supported by the Japan Society of Promotion of Science (JSPS).
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