Dangling-bond spin relaxation and magnetic 1∕f noise from the amorphous-semiconductor/oxide interface: Theory

We propose a model for magnetic noise based on spin flips (not electron trapping) of paramagnetic dangling bonds at the amorphous-semiconductor/oxide interface. A wide distribution of spin-flip times is derived from the single-phonon cross-relaxation mechanism for a dangling bond interacting with the tunneling two-level systems of the amorphous interface. The temperature and frequency dependence is sensitive to three energy scales: The dangling-bond spin Zeeman energy (δ), as well as the minimum (E_min) and maximum (E_max) values for the energy splittings of the tunneling two-level systems. At the highest temperatures, k_BT⪢max (δ,E_max), the noise spectral density is independent of temperature and has a 1∕f frequency dependence. At intermediate temperatures, k_BT⪢δ and E_min⪡k_BT⪡E_max, the noise is proportional to a power law in temperature and possesses a 1∕f^p spectral density, with p=1.2–1.5. At the lowest temperatures, k_BT⪡δ, or k_BT⪡E_min, the magnetic noise is exponentially suppressed. We compare and fit our model parameters to a recent experiment probing spin coherence of antimony donors implanted in nuclear-spin-free silicon [ T. Schenkel et al. Appl. Phys. Lett. 88 112101 (2006)], and conclude that a dangling-bond area density of the order of 10¹⁴ cm⁻² is consistent with the data. This enables the prediction of single spin qubit coherence times as a function of the distance from the interface and the dangling-bond area density in a real device structure. We apply our theory to calculations of magnetic flux noise affecting superconducting quantum interference devices (SQUIDs) due to their Si∕SiO₂ substrate. Our explicit estimates of flux noise in SQUIDs lead to a noise spectral density of the order of 10⁻¹² Φ₀²(Hz)⁻¹ at f=1 Hz. This value might explain the origin of flux noise in some SQUIDs. Finally, we consider the suppression of these effects using surface passivation with hydrogen, and the residual nuclear-spin noise resulting from a perfect silicon-hydride surface.