## 3 Technology Modules
### Fabrication of the Silicon Nano-Ridge  
The silicon nano-ridge is fabricated by employing anisotropic wet-etching of crystalline silicon in a tetramethylammonium hydroxide (TMAH)-based solution and local-oxidation of silicon (LOCOS). The starting material is a Czochralski-grown, \(<\)100\(>\)-oriented 4\({}^{\prime\prime}\) silicon wafer. A standard cleaning procedure, consisting of piranha, SC-1, and SC-2, is carried out. After stripping the native/chemical oxide, silicon nitride is grown thermally in ammonia in a rapid thermal processing (RTP) chamber with high-vacuum capability. Despite its low thickness (\(\sim\) 3 nm), thermally-grown silicon nitride exhibits an extremely low etching rate in TMAH and excellent impermeability to oxygen. Subsequently, electron beam lithography in combination with reactive ion-etching is used to define a line-pattern along the [110] direction, as illustrated in Figure 3a. After resist removal and directly after an additional short buffered oxide etch, TMAH (25 wt%) mixed with surfactant (isopropyl alcohol) is used to anisotropically etch the exposed silicon area at 80 \({}^{\circ}\)C. Figure 3b shows a trapezoidal structure bounded by two [111] facets formed due to the distinct etch-rate anisotropy of different crystallographic planes [40]. The inset in Figure 3a and the edge of the line structure in Figure 3b show a small undercut of the nitride hard mask due to the low etching rate of [111] facets. This is beneficial for reducing the line-edge-roughness of the line structure induced by imperfections of the initial lithography step. In order to obtain a quantitative measure of the surface roughness of the wet-etched (111) facets, atomic force microscopy (AFM) is used. The measurement is performed on a large step structure (step height \(\sim\) 800 nm) formed by two [100] facets and a (111) facet. A silicon cantilever (nominal tip radius 10 nm, cone angle 40 \({}^{\circ}\)) is used to profile the tapered (111) surface in tapping mode (nominal values: resonance frequency 325 kHz, constant force 40 N/m). The tip axis is tilted by 15 \({}^{\circ}\) with respect to the substrate normal in order to facilitate the imaging of the (111) facet. Figure 3c shows an AFM image and a line-cut of the wet-etched (111) facet in a scanning area of 800 nm\(\times\)250 nm. The measured root-mean-squared (RMS) = 0.3992 nm is well within the range of a commercial prime-grade silicon wafer (RMS = 0.2-0.8 nm) [41]. This top-down CMOS-compatible fabrication technique yields a high-quality trapezoidal nanostructure with minimal plasma damage and smooth surfaces comparable to a commercial prime-grade silicon wafer. In order to form a tip on top of the trapezoidal structure that not only allows the formation of a single QD, but also facilitates the generation of two corner-states located opposite of each other, dry oxidation in oxygen is carried out at 1050 \({}^{\circ}\)C. As a result of oxygen diffusion at the edges of the silicon nitride mask, a so-called bird's beak is formed from both sides, yielding the desired tip geometry of the nano-ridge (displayed in Figure 3d). The oxidation temperature is chosen to be higher than the viscous flow point to grow a relatively thick oxide in order to minimize the degradation of the Si/SiO\({}_{2}\) interface due to roughness induced by the oxidation process [42; 43]. Note that the formation of the bird's beak and hence the geometry of the tip region of the nano-ridge can be adjusted with the thickness of the silicon nitride layer. Indeed, a nitride thickness (\(>\)75 nm) completely suppresses the formation of a bird's beak [44]. As a result, choosing an appropriate nitride thickness in combination with the oxidation process allow manipulating the geometry and thus the electrostatic potential of the tip-region employed for the generation of QDs.