Three-dimensional photonic crystals fabricated by simultaneous multidirectional etching

We discuss three-dimensional (3D) photonic crystals fabricated by simultaneous multidirectional plasma etching. First, we investigate a method for controlling the ion sheath used in reactive ion etching for obtaining multidirectional etching. We then discuss the fabrication tolerance from an analytical perspective. Based on our results, we demonstrate the fabrication of 3D photonic crystals with thicknesses of 1, 1.5, and 2 lattice periods in the surface-normal direction on single-crystalline silicon wafers, which show high reflectance $(\sim 100\%)$ and low transmittance $(-17\mathrm{dB})$ at optical communication wavelengths, suggesting the formation of a complete photonic band gap. We reveal that the shape of the etched holes limits the performance of 3D photonic crystals and suggest possible ways to improve the band-gap effect. Moreover, we show that 3D photonic crystals with short lattice constants show high reflectance $(\sim 80\%)$ at visible to near-infrared wavelengths. By investigating the influence of absorption on the characteristics of 3D photonic crystals, we reveal that the reflectance remains as high as 94% in the photonic band-gap range even when the absorption of silicon is taken into account. We find that a unique increase of absorption occurs at several discrete wavelengths below the photonic band gap, suggesting the possibility of manipulating light absorption. These results not only simplify the fabrication of 3D photonic crystals, but also provide a basis for realizing 3D photonic nanostructures that include other materials.

Figure 1

Schematic picture of multidirectional etching technique for fabricating 3D photonic crystals. (a) Schematic structure of a 3D photonic crystal. (b) Picture of ion-sheath control plate for three-directional, simultaneous etching.

Figure 2

Calculated space-charge and potential distributions inside the ion sheath during the RIE process. (a) Space-charge distribution. (b) Potential distribution.

Figure 3

Calculated angular spreading of ions arriving to the surface of semiconductor. (a) Without ion-sheath control plate. (b) With ion-sheath control plate.

Figure 4

Calculation of photonic band gap (PBG) of 3D phonic crystals by simultaneous multidirectional etching. (a) Band structure of 3D photonic crystal. Inset shows the first Brillouin zone. (b) PBG range as a function of etching angle. (c) PBG width as a function of etching angle.

Figure 5

Fabrication tolerance of etching hole's shape. (a) Structural parameters of etching hole's shape used to examine fabrication tolerance. (b) Calculated PBG width as a function of r and $r^{\prime }/r$.

Figure 6

Fabrication tolerance of azimuth angle in angled etching. (a) Structural parameters of the change of azimuth angle with respect to the triangular lattice pattern. (b)–(d) Calculated transmittance in the case of thickness $1a_z, 2a_z$, and $3a_z$, respectively.

Figure 7

SEM images of fabricated 3D photonic crystal. (a) Top view. (b) Cross-sectional view. Panels (a) and (b) are cited from Ref. [22].

Figure 8

Measured optical properties of 3D photonic crystals fabricated by simultaneous three-directional etching with different etching time. (a)–(c) Reflectance and transmittance spectra of the structures with the thicknesses of $\sim 1a_z, \sim 1.5a_z$, and $\sim 2a_z$ obtained by increasing the etching time, respectively. The data in (a) and (b) are cited from Ref. [22]. The insets show top-view SEM images.

Figure 9

Calculation of reflectance and transmittance spectra considering the structural fluctuation in the fabricated structure. (a)–(c) Calculation for the structures shown in Figs. 8–8, respectively. Insets show cross-sectional image where we considered the tapering of the etching hole.

Figure 10

Influence of etching hole's tapering in 3D phonic crystals by simultaneous multidirectional etching. (a) Structural parameters of etching hole's taper used to examine fabrication fluctuation. (b) Dependence of minimum value of transmittance on 3D photonic crystal's (PC's) thickness.

Figure 11

Transmission spectra for various incident angles. (a) Measurement results. Inset shows the measured angles of transmittance. (b) Calculation results of transmittance and photonic band diagram.

Figure 12

Demonstration of 3D photonic band gap in wavelengths below 1.1 $\mu \mathrm{m}$. (a)–(d) Top-view SEM images for lattice constants ranging 450–315 nm. (e)–(h) Measured reflectance of structures shown in (a)–(d). Panels (a)–(h) are reprinted from Ref. [22].

Figure 13

Calculation of the influence of material absorption on the optical characteristics of 3D photonic crystals. (a) Refractive index and extinction coefficient of single-crystalline silicon. (b)–(e) Dependence of reflection characteristics on lattice constant. (f) Summary of maximum reflectance in photonic band-gap range.

Figure 14

Influence of both the material absorption and the tapering of etching hole on the characteristics of a 3D photonic crystal with the band gap at $\sim 600$ nm. (a) Calculation result. (b) Measurement result.

Figure 15

Absorption characteristics of 3D photonic crystal. (a) Absorptivity spectra for different thicknesses of 3D photonic crystal. (b) Photonic band diagram for wave number in surface-normal direction.