Pressure dependent etching

Next, we turn to the pressure dependence. In Figure 4.2A, AFM topography images are shown at four dierent pres-sures p at constant distance. The number of holes increases with decreasing pressure, similar to decreasing distance, giv-ing rise to etch pits of monolayer step height at intermediate pressures. At the highest pressures, however, no etch pits where observed, in strong contrast to the lowest pressure,

1.7 mbar 1 mbar

1.4mbar 0.7mbar

Figure 4.2: Pressure dependence of graphite plasma exposures (A) AFM images (tapping mode) of graphite surfaces for various p, as indicated, exposed for one hour at d = 52 cm, shown on the same color scale. All panels are 3 × 3 µm², the scale bar is 1 µm. (B,C) Histograms from 10 × 10 µm²scans, displaying the number of holes against hole diameter (bin size 20 nm) for pas labeled. (D) Length Lgof the optically visible plasma as a function of p. The dashed curve is a 1/√

pt. (E) Number of holes versus distance from plasma edge d − Lg. A lower bound of 300 holes is given for the heavily etched cases where an exact hole-count was not feasible. The dashed black line is an exponential t to the data with < 300 holes.

where ubiquitous and deep etching is seen, demonstrating the strong inuence of p. Analyzing the etch pits using his-tograms conrms that p and d have a similar inuence on the etching process, compare Fig. 4.2B, C with Fig. 4.1B-D. In addition, Figure 4.1E summarizes the histograms of all inves-tigated graphite samples, using color to represent the

num-ber of holes, while the size of each marker is proportional to the width of the distribution of hole diameters. A clear cor-relation between the number of holes and the width of the distribution is seen, i.e. the largest circles (large width of distribution) are all red (large number of holes), while small circles are purple. This means that a large ion ux (creating holes) goes together with large radical ux (large anisotropic etch rate).

The analysis of the graphite exposure data leads to two quali-tatively dierent types of processes: the direct and the remote plasma regime. In the direct plasma regime (large, red circles, Fig. 4.1E), the sample is located directly within the plasma discharge region, hence exposing it to large densities of rad-icals and ions, capable of inducing defects. In the remote plasma regime (small, purple circles, Fig. 4.1E), on the other hand, the sample is positioned outside, downstream of the plasma generation region, where ions have recombined and only a residual ux of radicals is present. There, anisotropic etching proceeds predominantly from preexisting defects and step edges, leaving the basal planes mostly untouched.

Further, there is an intimate connection between distance and pressure: lower pressure results in a longer gas mean free

path and therefore a larger average distance for recombina-tion in the diusive gas. This results in a larger size Lg(p) of the plasma, measured from the edge of the visibly glow-ing plasma to the surfatron, see Fig. 4.2D. Thus, changglow-ing the pressure with xed sample position modies the distance between sample and plasma edge. Hence, it is useful to in-troduce an eective distance d⁰ = d − Lg(p), the distance from sample to the edge of the glowing plasma. Thus, d⁰. 0 roughly marks the direct plasma regime while d⁰ 0signies the remote plasma regime. Reactive particles are generated inside the plasma column and start recombining once they have left the plasma generation region.

The reaction kinetics in low temperature H-plasmas are highly non-trivial despite the relatively simple chemical composition[89]. Nevertheless, it is well known that at the pressures used here (p ∼ 1 mbar), the predominant radical decay mechanism is mainly surface mediated association rather than gas collisions. Two colliding H atoms require a third body to carry away the excess energy for association to occur [126]. However, under the present conditions, three body collisions are very unlikely, thus leaving only the surface assisted process (which also leads to surface

heating[77]). Recombination of ions, in contrast, can also occur through through an additional collisional channel, in absence of a surface. Which species  ions or radicals  decay on a shorter length scale downstream of the plasma edge thus depends on both the surface properties and gas parameters.

For anisotropic etching without defect creation, a ux of H radicals in absence of ions is needed, thus requiring the ion density to decay on a shorter length than the radicals.

The surface-attenuation of hydrogen thus plays an important role, and was previously studied [77, 127]. Quartz  as used in our experiments  was identied as a material with a rela-tively low recombination coecient, particularly compared to some common metallic surfaces (stainless steel, Aluminum).

This weak surface attenuation can open a downstream win-dow oering a ux of H radicals (not decayed yet) in absence of ions (almost all decayed), as desired and achieved here, see e.g. Fig. 4.1B and 4.2B. We note, however, that even a rela-tively small amount of metallic deposition on the surface of the tube can signicantly enhance the surface decay of radi-cals, and potentially close this window, i.e. the radicals decay before the ions.

To study the decay of the reactive species, we note that the ion intensity is proportional to the number of holes created, shown in Fig. 4.2E as a function of distance from the plasma on a log-lin plot for all 5×4 combinations of p and d parame-ters. We nd a roughly exponential decay with distance, with a 1/e decay length of about 5 cm. A similar decay is seen for the width of the diameter distribution, which is also propor-tional to the ion intensity (see SOM), giving the same decay length within the error bars. The decay is expected to satu-rate once the intrinsic, preexisting graphite defect density is reached. Further, changing p also alters the decay length by aecting the mean free path and diusion constant [77], but for the narrow range of pressures used in the present data set, this is not a very large eect.

The anisotropic etch rate, on the other hand, is related to the intensity of H radicals. However, the presence of ions (in most of the present (d, p) data set) can enhance the etch rate, impeding extraction of the decay length of radicals. Never-theless, we extract the anisotropic etch rate, dened as the growth per unit time of the radius of a circle inscribed to the hexagonal etch pit, averaged over several holes, shown in Fig. 4.4A. Only the largest set of hexagons of each exposed

SL on SiO₂

phase [°], height x0.25 [nm]

SL on hBN

Figure 4.3:SL/BL and substrate dependence(A,B) AFM phase contrast images of a SL (A) and BL (B) section of the same ake on a Si/SiO2 substrate, etched for 1 h at T = 450^◦C. Holes of 50 nm diameter were dened before etch-ing. (C,D) AFM topography images of a SL ake on hBN etched for 3 h (C) and 5 h (D). Holes of 200 nm were

de-ned before etching. All images are 2 × 2 µm², the scale bar is 1 µm.

graphite sample were evaluated to obtain the etch rate, since smaller holes might not have etched from the beginning of the exposure. As expected, the anisotropic etch rate is largest for small distances, falling o with increasing separation from the plasma edge.