At high ion fluences, which are 1 × 10¹⁷/cm² for 0.02-Ω·cm, and 1 × 10¹⁶/cm² for 0.4-Ω·cm wafers, the defect density along the irradiation regions from the top surface to the end-of-range region is high enough to completely inhibit the electrochemical etching processes with the above etching conditions. As shown in Figure 1a, irradiation of 1-MeV protons with a high ion fluence in bulk silicon results in defect regions with high-enough density along the full range of 16.3 μm, which protons can penetrate. During electrochemical etching process, porous silicon is selectively formed in the nonirradiated regions, as shown in Figure 1b. The etching time for different current densities and wafer resistivity was well controlled to keep the etching depth less than 16.3 μm. After removal of porous silicon in KOH solution, silicon structures on the substrate were obtained, as in Figure 1c.

Patterns with square lattice of silicon pillars were designed with different periods for proton beam writing. Figure 2a shows a scanning electron microscope (SEM) image at 25° tilt. A 0.4-Ω·cm wafer was irradiated with a square lattice pattern with a 2-μm period using 1-MeV protons, which were focused to 400 nm in both directions, with fluence 5 × 10¹⁶/cm². After etching with 60 mA/cm² for 5 min and removing porous silicon with a KOH solution, silicon pillars in Figure 2a were obtained. In Figure 2b, a 0.4-Ω·cm wafer was irradiated with a square lattice with a larger period of 4 μm and a smaller beam size of 200 nm, with the same fluence, and etched for 6 min at the same current density.

Figure 3 shows the defect density distribution versus depth for 250-keV and 1-MeV protons in silicon from Stopping and Ranges of Ions in Matter (SRIM) simulation 22. Most of the defects concentrate at the end-of-range regions where the ions stop. At a moderate fluence for 250-keV protons, regions with high-enough defect density to inhibit formation of porous silicon are only located at a depth around 2.4 μm; thus, buried silicon wires form surrounded by porous silicon.

To obtain freestanding structures, a high-energy proton beam of 1 MeV, which has a deep penetration depth in silicon, was used to irradiate lines with an extremely high fluence, 1 × 10¹²/cm, at the same area which function as supports, as in Figure 4a. Line fluence is used here in the line irradiation case where the size of ion beam is smaller than the lateral width of high defect regions. In subsequent electrochemical etching, the etching time and current density for different resistivity wafers were carefully controlled to completely undercut the end-of-range regions of 250-keV protons, but not reach the end-of-range of 1-MeV protons, as in Figure 4b. Subsequent dipping in dilute KOH solution removed the porous silicon, and freestanding silicon wires supported by thick walls were obtained, as in Figure 4c. Figure 4d shows freestanding silicon wires with three different spacings, where 250-keV protons were focused to 100 nm and irradiated with a line fluence of 1 × 10¹¹/cm. Based on this, fabrication of a 2D photonic slab of a square lattice of air holes in a silicon matrix was designed.

Two sets of lines were irradiated horizontally and vertically in the same area using 250-keV protons on 0.02-Ω·cm silicon wafers to create defect distribution, as shown in Figure 5a, in which the defect density at the intersecting parts of the lines is doubled. Thus, in the etching process, the surrounding area of the intersecting part is not etched as well, giving rise to the formation of porous silicon in circular regions, as shown in Figure 5b. After 4 min of etching with a current density of 40 mA/cm² and a subsequent removal of porous silicon, a freestanding 2D photonic slab with a square lattice of air hole in silicon matrix was obtained, as shown in Figure 5c. This structure was fabricated with an ion fluence of 8 × 10¹⁰/cm with a period of 1.5 μm.

By tuning the energy of ions, end-of-range regions with high defect density at moderate ion fluence can be generated at different depths in the wafer, and after a subsequent electrochemical anodization, silicon wires at different depths of the silicon wafer were obtained. SRIM 22 calculations in Figure 6a show that the range of protons in silicon varies from 1.8 to 16.3 μm when the proton energy increases from 200 keV to 1 MeV.

Here, we propose the fabrication of a 3D woodpile structure using proton beam writing to generate end-of-range regions with high defect density at different depths. In order to fabricate woodpile structure with one period, protons with four different energies, E₁, E₂, E₃, and E₄, will be required to irradiate lines in the same area with suitable fluence and alignment, as shown in Figure 6b. Figure 6c shows an initial result on two-layer freestanding silicon wires in two directions using 250 and 200-keV protons, respectively, in 0.02-Ω·cm silicon wafers supported by thick walls from 1-MeV protons. By carefully controlling the alignment, ion energy, ion fluence, and etching current density, a 3D woodpile structure with complete band gap lying in the mid-infrared (IR) range should be possible.

Figure 7a,b shows the computed 2D PBS for the experimental structures shown in Figure 2a,b, respectively. In both figures, a TM photonic gap opens between the first and second band. However, the gap size is much higher in Figure 7b. This is due to the different concentration factors in both structures. In Figure 7b, the radius of the Si pillars is r = 0.1a, where a is the lattice period, and the gap opens from 0.422 to 0.495 of the normalized frequency. While the radius of the Si pillar in the structure of Figure 7a is r = 0.415a, the gap opens from 0.210 to 0.218 of the normalized frequency. As the first photonic band concentrates its energy in the high-dielectric-constant region, i.e., in the Si pillar, the second band concentrates its energy in the low-dielectric-constant region in order to be orthogonal to the first band 3. When the ratio r/a is smaller, the different concentration factors between both bands increase, and the gap size is higher. If the radius of the Si pillar is too small, the first band cannot concentrate its energy in them, and the gap disappears.

On the other hand, in Figure 7a, other gaps open at higher frequencies. Between the third and fourth bands, a gap opens from 0.345 to 0.365 of the normalized frequency, and between the sixth and seventh, from 0.513 to 535. However, no TE gap opens in either structure. The flexibility of the fabrication process allows varying the radius of the Si pillar and the lattice period to tune the frequency ranges where the gaps can be opened for a specific application.

In this case, as a freestanding structure was studied, novel approaches were needed. First, the eigenstates of the slab were calculated using a z-supercell approach, where guided bands were unaffected. Then, the light cone was obtained and overlapped 28.

Figure 8 shows PBS for TE-like modes; bands with even symmetry respect reflections through a z plane (z directions being the height slab direction) for the photonic slab of air holes with square lattice in silicon matrix shown in Figure 5c, with r/a = 0.3125 and h/a = 0.75, where r is the radius of the air hole, h is the thickness of the slab, and a is the period of the lattice.

It shows two gaps around normalized frequency a/λ = 0.26 and 0.29, where a = 1.5 μm. PBS for TM-like modes shows no gap. The frequency range and gap size can be tuned and optimized by varying irradiation and etching conditions. Photonic crystal structures based on this approach of selective formation of porous silicon have an extra degree of tuning from porous silicon, where removal process of porous silicon in KOH etching is not conducted instead. Figure 9 shows the gap map of porosity for a photonic slab of square lattice of porous silicon hole in silicon matrix, with r/a = 0.3125 and h/a = 0.75, where r is the radius of the porous silicon hole, h is the thickness of slab, and a is the period of lattice.