# High-Aspect-Ratio Silicon Metasurfaces: Design, Fabrication, and Characterization. _Applied_
## 2 Design of the Transmissive Silicon Meta-Atom  
We start by presenting how to design the transmissive THz silicon meta-atom exhibiting high transmittance, a high polarization conversion ratio and a transmission phase covering a sufficiently large range, which can be the basic element to construct performant metasurfaces with different functionalities [17; 24; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38]. Although silicon structures using Mie resonances can manipulate the transmission amplitude and phase [43; 44; 45; 46], it is very difficult to achieve these requirements simultaneously with low-AR silicon design. As demonstrated in our recent work [39], though the silicon pillar structure with high AR can well achieve the above-mentioned demand, it is impossible to fabricate it in free-standing geometry. In practice, the micro-pillar should be deposited or etched on a substrate, and the presence of a substrate will dramatically modify the performance of the free-standing meta-atoms design. To clarify this point, we perform a full-wave simulation to demonstrate the polarization conversion effect of free-standing meta-atoms and the micro-pillar with a substrate, which are arranged in a square lattice with a periodicity of 157 \(\upmu\)m (with following geometrical parameters: \(\mathrm{H}=400\), \(\mathrm{h}=30\), \(\mathrm{d}_{1}=\mathrm{d}_{2}=132\), \(\mathrm{w}_{1}=33\), \(\mathrm{w}_{2}=50\), \(\mathrm{d}_{3}=62\), all in units of \(\upmu\)m). Here, we take the meta-half-wave-plate (MHWP) design as an example. As shown in Figure 1b, the metasurface composed of the free-standing micro-pillars can function well as a half-wave-plate (HWP) with a polarization conversion ratio (PCR) (PCR=\(\left|\left(\mathrm{t}_{\mathrm{xx}}-\mathrm{t}_{\mathrm{yy}}\right)\right|^{2}/4\), where \(\mathrm{t}_{\mathrm{xx}}\) and \(\mathrm{t}_{\mathrm{yy}}\) denote the complex transmission coefficients for the x- and y-polarized waves) near to 1 at a working frequency of 0.65 THz, where all the input power of the incident right circular polarized (RCP) THz wave can be fully converted into the left circular polarized (LCP) component. Actually, the presence of the substrate largely modifies the PCR performance of the ideal free-standing MHWP, as illustrated by the blue line in Figure 1b, which was associated with the additional reflection induced by the impedance mismatch at the interface of the substrate and air. To compensate such an effect, the carefully designed silicon micro-resonators are added to another side of the substrate as an anti-reflection layer, which can efficiently reduce the reflections induced by the substrate. Consequently, as shown in Figure 1a, our proposed meta-atom consists of three silicon layers, including a 400 \(\upmu\)m high micro-pillar with a rectangular cross-section, a 62 \(\upmu\)m thick continuous substrate and a 30 \(\upmu\)m high micro-resonator with optimized dimensions to obtain high transmission for the whole meta-atom design at the desired working frequency. One can see that our tri-layered meta-atom design exhibits almost perfect HWP performance at 0.65 THz and a working bandwidth of about 0.1 THz. It is worth mentioning that by changing the geometrical parameters of a tri-layered meta-atom with high AR, one can realize many different functionalities, with high transmittance and large transmissive phase coverage, such as meta-lens and beam deflectors. In practice, the fabrication of tri-layered all-silicon metasurfaces with such high AR can technically be carried out by conversional photolithography and plasma etching in the Bosch process with an altering multi-stepped etch cycle and passivation cycle [40; 41; 42], as shown in Figure 1c. However, it is quite difficult to achieve the perfect etching control in both the lateral and vertical direction for dielectric metasurfaces with high AR, which will determine the sidewall profile and vertical thickness distribution (VTD) (i.e., especially for the thickness of continuous substrate), respectively, as illustrated in Figure 1d.