Ab Initio Study of (100) Diamond Surface Spins

Unpaired electronic spins at diamond surfaces are ubiquitous and can lead to excess magnetic noise. They have been observed in several studies to date, but their exact chemical nature is still unknown. We propose a simple model to explain the existence and chemical stability of surface spins associated with the ${sp}^3$ dangling bond on the (100) diamond surface using density-functional theory. We find that the (111) facet, which is naturally generated at a step edge of (100) crystalline diamond surface, can sterically protect a spinful defect. Our study reveals a mechanism for annihilation of these surface spins upon annealing, consistent with recent experimental results. We also demonstrate that the Fermi-contact term in the hyperfine coupling is not negligible between the surface spins and the surrounding nuclear spins, and thus ab initio simulation can be used to devise a sensing protocol where the surface spins act as reporter spins to sense nuclear spins on the surface.

Figure 1

Top and side views of step models of (100)-$8\times 2$ diamond surface. (a) Chadi’s atomic step model. (b) Tsai’s atomic step model. (c) The formation enthalpy difference per unit step between Chadi’s and Tsai’s atomic step models as a function of hydrogen chemical potential. The red and blue regions represent that Tsai’s model is energetically more or less stable than Chadi’s model. The typical ($p,T$) parameters are in the range of $(20,1300)\dots (100,1300)$ for CVD growth of diamond, marked as the yellow region.

Figure 2

(a) Structure of Chadi’s step model. Side view (left) and top view (right) are presented. For the sake of clarity, only the topmost five layers is displayed in the top view and the color scheme is consistent with Fig. 1. (b) Energy levels of surface dangling bond state. Black and red dashes represent spin majority and minority channels, respectively. Blue and green regions represent valence and conduction bands, respectively.

Figure 3

Structure of carbon vacancy at step edge and its corresponding energy level plot. The “$X$” denotes the carbon atoms with coordination number of 3.

Figure 4

(a) Energy-level plot for a single vacancy on the $\mathrm{H}$-terminated diamond (100) surface. To compare the energy-level variations of single vacancies near the surface, a diamond model with a thickness of 22 layers is utilized. Site 0 and site 1 are employed to simulate bulk states. (b) Energy-level plot for a single vacancy on the $\mathrm{OH}$-terminated diamond (100) surface. In this case, a ten-layer thickness is introduced to investigate the surface states.

Figure 5

Structure details of single vacancy in the $\mathrm{H}$-terminated step model. The four carbon atoms surround the vacancy site are highlighted with light-green color.

Figure 6

The relative energy (unit in eV) of hydrogen saturation of surface vacancy. The four carbon atoms surrounding the vacancy site are highlighted with light-green color.

Figure 7

(a) Hydrogen saturation of surface vacancy. To assist with visual guidance, the additional hydrogen atoms are marked with symbols “*,” “$x$,” “$A$,” or “$B$.” (b) The reaction of hydrogen desorption from surface vacancy.

Figure 8

(a) Top and side view of step model of $\mathrm{C}$(100)-$6\times 6$ diamond surface. The critical $\mathrm{C}$ atoms are labeled by “+” and “*” before $\mathrm{OH}$ adsorption to $\mathrm{C}$(*). The (100) and tilted (111) facets are highlighted with red and blue colors, respectively. (b) Top view of surface-spin model. The DB position occurs for $\mathrm{C}$(+) after adsorption of the $\mathrm{OH}$ group to the $\mathrm{C}$(*) atom.

Figure 9

(a) Top view of three different surface-spin defect models. The color settings are the same as those in Fig. 8. (b) The HSE results of the energy levels of $\mathrm{O}$/$\mathrm{H}$/$\mathrm{H}$ model before and after $\mathrm{OH}$ desorption. (c) The HSE energy levels of three surface-spin defect models. The valence and conduction bands are depicted as blue and red regions, respectively. The valence-band maximum is aligned to zero. (d) The isosurface of the calculated spin density (isovalues are $5\times {10}^2\mathrm{e}/{\mathrm{Bohr}}^3$ in the main figure and $1.3\times {10}^4\mathrm{e}/{\mathrm{Bohr}}^3$ in the top-left inset) for surface-spin model. The spin density is clearly localized on the DB site. The carbon, oxygen, and hydrogen atoms are gray, red, and pink balls, respectively.

Figure 10

(a) Schematic illustration of surface-spin (green lobes) annihilation. After thermal annealing in vacuum, the $\mathrm{OH}$ radical desorbs from the surface trench site, causing surface reconstruction, and DB is eventually passivated. The color settings are the same as those in Fig. 8. (b) Calculated $\mathrm{OH}$ desorption rate of three models as a function of temperature. The annihilation temperatures of 465 and $600{}^{\circ }\mathrm{C}$ are denoted as dashed lines. The uncertainty in the frequency prefactor is considered by the gray area.

Figure 11

Energy level plots for the ${sp}^3$ defect in the function of slab thickness given by the number of layers.