Solution to Electric Field Screening in Diamond Quantum Electrometers

There are diverse interdisciplinary applications for nanoscale-resolution electrometry of elementary charges under ambient conditions. These include characterization of two-dimensional electronics, charge transfer in biological systems, and measurement of fundamental physical phenomena. The nitrogen-vacancy center in diamond is uniquely capable of such measurements, however electrometry thus far has been limited to charges within the same diamond lattice. It has been hypothesized that the failure to detect charges external to diamond is due to quenching and surface screening, but no proof, model, or design to overcome this has yet been proposed. In this work we affirm this hypothesis through a comprehensive theoretical model of screening and quenching within a diamond electrometer and propose a solution using controlled nitrogen doping and a fluorine-terminated surface. We conclude that successful implementation requires further work to engineer diamond surfaces with lower surface-defect concentrations.

Figure 1

Schematic of the three-layered model used to investigate field screening and $\mathrm{N}$-$V^{-}$ charge quenching. The external environment contains the ambient atmosphere and the charge distribution to be detected. Water vapor adsorbs to the diamond surface to form an adlayer which causes dielectric screening. This can be mitigated by passivating the diamond with fluorine, which exhibits strong dipolar hydrophobicity [50, 51]. Furthermore, fluorine-terminated diamond is chemically inert, room-temperature stable, and possesses a positive electron affinity [52]. While a (111) surface termination is depicted here, other fluorinated diamond geometries possess similar desirable properties. The surface itself contains a high density of ${\mathrm{sp}}^2$ surface defects which introduce acceptor levels into the diamond band structure [44]. These readily quench the $\mathrm{N}$-$V^{-}$ charge state and at partial occupation lead to strong surface-screening effects. Within the diamond, uncontrolled doping of $n$-type defects such as ${\mathrm{N}}_S$ lead to Debye screening [53].

Figure 2

Isotropic susceptibility of a water adlayer physisorbed on fluorine-terminated diamond as a function of surface coverage at 300 K.

Figure 3

Electric field screening ratio at a depth of 10 nm into diamond for varying water-surface coverage. This represents the ratio of the screened field magnitude relative to the unscreened field magnitude (i.e., within a vacuum) produced by a point charge $(q)$. In this model the water layer is 3 Å wide. The inset depicts the method of images used to determine the screening ratio. Here fictitious “image” charges (dashed $q\mathrm{s}$) are introduced to solve Poisson’s equation. The magnitude of the charges and their positions are such that they reproduce the electrostatic boundary conditions of the three stacked dielectrics, representing the diamond, water adlayer, and external atmosphere.

Figure 4

(a) Schematic of the toy-model electrometer. An $\mathrm{N}$-$V$ center (nitrogen represented as the blue sphere, vacancy as the gray sphere, and ground-state spin as the red arrow) is positioned a depth $d$ below a fluorine-terminated surface. A (100) diamond geometry is depicted. The surface possesses a density ${\sigma }_T$ of ${\mathrm{sp}}^2$ charge traps, which are preferentially saturated by a grounded ${\mathrm{N}}_S\delta$-doped layer positioned at a depth $D$. This generates a negative charge density at the surface subsequently forming a parallel plate capacitor. A linear potential extends throughout the capacitor with a magnitude $V_S(0)$ at the surface. (b) Energy-level diagram of defect states within the diamond electrometer. The acceptor level of the ${\mathrm{sp}}^2$ charge traps is raised by an energy $V_S(0)$, while that of the $\mathrm{N}$-$V$ center is raised by $V_S(0)(1-d/D)$. Charge stability of the $\mathrm{N}$-$V^{-}$ center requires full occupation of the charge traps and $E_{\mathrm{N}\text{−}V}+V_S(0)(1-d/D)\ll E_N$.

Figure 5

Occupation of surface traps and the $\mathrm{N}$-$V^{-}$ charge state as a function of surface-trap density for the toy-model electrometer. Here we assume that $D=100$ nm, $d=60$ nm, and $T=300$ K. Three different electrometer operational regions have been distinguished and are discussed in the text.

Figure 6

Screening and quenching mechanisms induced by ionization of ${\mathrm{N}}_S$ during optical control of the $\mathrm{N}$-$V$ center. The laser (532 nm) induces a density of ${\mathrm{N}}_S^{+}$ defects within the $\delta$-doped layer (depicted in pink), which subsequently generates a local positive potential (yellow contour lines) and ionizes free electrons into the lattice (orange circles). The local potential has the potential to reduce $\mathrm{N}$-$V^{-}$ charge stability while the modulating charge density interferes with $\mathrm{N}$-$V$ spin dynamics during quantum sensing. There is also a lower risk of $\mathrm{N}$-$V^{-}$ charge destabilization due to scattering with Auger electrons. Erroneous $\mathrm{N}$-$V$ centers present in the doped layer can also introduce background counts during readout (red photon) which increases measurement contrast leading to lower sensitivity.

Figure 7

Schematic of a diamond-based electrometer for subnanometer-resolution charge imaging at ambient temperatures. A shallow $\mathrm{N}$-$V^{-}$ spin probe detects the electric field from an elementary charge positioned above the surface through optically detected magnetic resonance. Primal ${\mathrm{sp}}^2$ defects present on the surface with density ${\sigma }_T$ act as electron traps, quenching the $\mathrm{N}$-$V^{-}$ charge state and causing detrimental screening when partially occupied. This is systematically controlled by saturating the charge traps using a sacrificial layer of $\delta$-doped ${\mathrm{N}}_S$ positioned a depth $D$ into the substrate. A ${\mathrm{N}}_S$-deficit disk of radius $r$ allows for optical initialization and readout of the $\mathrm{N}$-$V^{-}$ without ionizing mobile charge carriers from the $\delta$-doped layer. The laser (532 nm) is incident from beneath the electrometer opposite of the sensing side.

Figure 8

Maximum viable surface-trap density (${\sigma }_T$) as a function of $\delta$-doped ${\mathrm{N}}_S$ layer depth and hole radius for the electrometer design presented in Fig. 7. Trap densities in excess of those presented here result in an electric field screening ratio lower than 99% (i.e., the field is screened greater than 1% of its unscreened value).