## 3 Results and Discussion
### Characterization of Morphology and Chemical States of Polycrystalline Diamond Films
#### 3.1.3 Secondary Ion Mass Spectrometry (SIMS) Analysis  
Figure 4 shows two examples of the secondary ion mass spectrometry (SIMS) spectra from analyses of PCD films A and E, which have over an order of magnitude difference in grain size. The SIMS measurements show that the C atom concentration, as a function of depth from the surface, is constant for all films around \(10^{23}\) atoms/cm\({}^{3}\) (Figure 4 red line), while the H atom concentration decreases as the grain size of the PCD films increases (see Figure 5, black lines). An increased H\({}_{2}\) flow did not result in an increase in H incorporation in the sample. The availability of H during crystal growth was not a limiting factor, as evidenced by the insensitivity of H\({}_{2}\) flow on H atom incorporation. The H atom concentration vs. grain size is plotted in Figure 5 (see left \(y\)-axis). Figure 3: Grain size for PCD films (samples A–G from Table 1). The grain sizes of PCD films A and B were determined using the XRD peaks, while for PCD films C to G the grain sizes were determine using SEM analysis. A simple order-of-magnitude calculation was performed assuming two dangling bonds per diamond unit cell (one per each C atom) on either side of the grain boundary, and a homogeneous grain size for each of the samples. The density of C atoms dangling bonds in the sample (\(D\)) was calculated using Formula (3) below:  
\[D=\frac{s\ N\ b}{V}=\frac{\left(6\ l^{2}\right)\left(\frac{V}{P}\right)\left( \frac{2}{\sigma^{2}}\right)}{V}=\frac{12}{\left(l\ a^{2}\right)} \tag{3}\]  
Figure 4: Spectra from SIMS analysis for PCD films with different grain sizes (A and E) show the C and H element distribution and content through the depth of the PCD films. The O and Si atoms from the SiO\({}_{2}\) layer on the Si substrate are present at the substrate–film interface. (**a**) Sample A, UNCD, (**b**) Sample E, MCD. Figure 5: C and H atom concentration [H] vs. PCD film grain size, and number of dangling bonds per site. [H] data are extracted from Sims measurements. The solid line indicates the calculated density of dangling bonds assuming 2 C atom dangling bonds per unit cell per bulk sample volume. where \(s\) is the surface area of a diamond single crystal, \(N\) is the number of crystals in a unit volume, \(b\) is the number of C atom dangling bonds per area, \(V\) is the volume of the sample (for example 1 cm\({}^{3}\)), \(l\) is the grain size, and \(a\) is the diamond lattice constant. This simple function is plotted on the secondary axis of Figure 5 (solid line). The good alignment between the calculated density of the dangling bonds and the H atom concentration supports the hypothesis that H atoms are incorporated primarily into the grain boundaries rather than into the bulk of the diamond crystalline grains. The higher concentration of H atoms in UNCD vs. MCD films can be explained by the increased availability of C atom dangling bonds in the grain boundaries of UNCD films. The data and calculations presented in Figure 5 indicate that the available sites for H atom insertion in grain boundaries are dominated by geometrical features. C atom dangling bonds are passivated by the introduction of H atoms, suggesting that the surface of the crystalline diamond grains is the primary location of incorporation of H atoms. The slope of the density of dangling bonds (sites/cm\({}^{3}\)) per grain size (Figure 5 solid line) is the surface concentration of dangling bonds, and it is calculated to be 1.56 \(\times\) 10\({}^{15}\) sites/cm\({}^{2}\). Assuming that the nature of all grain boundaries, regardless of grain size, is similar, the concentration of H atoms per unit area should be the same. Calculations of the surface concentration of H atoms per unit area show that the values for all the PCD films in this study are between 1 \(\times\) 10\({}^{15}\) and 3 \(\times\) 10\({}^{15}\) atoms/cm\({}^{2}\).