Charge-state stability of color centers in wide band gap semiconductors

Investigating the initialization and readout of relative populations of NV− and NV0 defects in diamond

“…In this case, there is no distribution factor for hole occupation given that the presence of an ionizing potential implies that the ionized state of the donor is favored and that the electron should not fully rebind to the donor that led to the ionization of the acceptor. The lack of spontaneous charge conversion from NV 0 to NV À in the work of Yuan et al 78 for NV centers that were initialized to NV 0 can be explained by the fact that our formalism 77 implies that the timescale for spontaneous conversion from NV 0 to NV À will be much faster than the shortest time after which the NV À population was assessed in the Yuan et al experiment. Furthermore, the steady-state relative populations of NV À and NV 0 in that experiment and the corresponding values of the Fermi level imply the presence of dopants other than substitutional N to which the charge of the NV À could be stably transferred.…”

“…Indeed, if the charge transfer is induced by phonon modes then the phonon modes supply the requisite kinetic energy of the model from our earlier work. 77 In our prior work, 77 we had also noted that the phonons would thermalize the electronic degrees of freedom. We had described the electronic motion using two degrees of freedom, namely, a radial degree of freedom r and an angular degree of freedom θ.…”

“…Given the proximity to neighboring defects, we have found that charge-state decay experiments for ionized color centers in wide-bandgap semiconductors are better described by tunneling directly between defect states without the intermediary of the crystal band edges. 77 In that case, we can write the effective rate as…”

“…r is the radial velocity obtained from integrating the equation of motion for an electron initially experiencing an electrostatic force having q cos(θ) and where r 0 is the distance between the donor and the acceptor. 77 The positive sign in the expression for dr dt is employed if the initial velocity of the electron is away from the other dopant while the negative sign is employed if the initial velocity of the electron is toward the other dopant.…”

“…(E F D þ 3:4 eV)=2 from our earlier work. 77 The value 3.4 eV is the surface level associated with an ether-like termination of the diamond surface measured relative to the valence band maximum. [80][81][82] In Ref.…”