Unresolved mechanisms in the electrical detection of the spin resonance of a single electron trap in a silicon field-effect transistor (Xiao et al., 2004)

In 2004, Xiao, Martin, Yablonovitch and Jiang demonstrated electrical detection of the electron spin resonance (ESR) of a single paramagnetic center formed by a defect in the gate oxide of a commercial silicon n-channel field-effect transistor: the spin orientation was converted into a change of trap charge state, read out as a change of the channel current through a random telegraph signal. The experiment left four specific issues unresolved, which the intervening literature has not settled. First, the dominant mechanism of the nonlinear ESR response observed at high Rabi frequency ($\gamma H_1$ of order 10 kHz, comparable to the trap tunneling rate of about 20 kHz), in which the sign of the change in trap occupancy probability inverts and the tunneling rate is modulated by up to about 10%, has not been identified; non-resonant microwave-induced changes of the trap rates remain a competing, unexcluded explanation. Second, the origin of the extracted spin-spin relaxation time $T_2$ of about 0.1 μs, versus tens of microseconds for isolated paramagnetic centers in SiO$_2$, has not been decomposed into interaction with channel electrons versus microwave power broadening. Third, microwave heating that raises the effective electron temperature to about 1.5 K at a 0.4 K bath still limits the sensitivity of this platform, and the remedies the source paper proposed (g-tensor modulation or pulsed high-frequency sources) have not been implemented for it. Fourth, the microscopic identity of the paramagnetic center, with $g = 2.02 \pm 0.015$ matching no known Si/SiO$_2$ defect, remains unknown. Adjacent later work (readout-dynamics theory, quantified non-resonant microwave effects on trap rates, long-coherence pulsed electrically detected magnetic resonance of donors, broadband EDMR, and single-shot donor and quantum-dot spin readout) touches each issue in other systems without closing the stated questions.

Background

Electron spins in silicon are attractive carriers of quantum information because silicon has weak spin-orbit coupling and (in isotopically purified $^{28}$Si) can be nearly free of nuclear spins, so that donor electron spins can remain coherent for very long times (for phosphorus donors, spin relaxation times up to seconds at low temperature were measured by Tyryshkin et al., 2003). Realizing spin-based devices nevertheless requires reading out and manipulating a single electron spin electrically, in a structure compatible with silicon integrated-circuit technology. Xiao, Martin, Yablonovitch and Jiang (Nature 430, 435, 2004) addressed exactly this by using a defect in the gate oxide of a standard commercial n-channel metal-oxide-semiconductor field-effect transistor (MOSFET).

The physical ingredient they exploited is a long-studied one: in small MOSFETs, individual traps near the Si/SiO$_2$ interface capture and emit channel electrons one at a time, producing a random telegraph signal (RTS), a two-level random switching of the source-drain current first mapped out systematically in the low-frequency-noise literature (Kirton and Uren, 1989). The relevant paramagnetic defects at and near the Si/SiO$_2$ interface are also long known: $P_b$ centers (silicon dangling bonds at the interface, with g-factors around 2.003 to 2.007) and $E'$ centers (oxygen-vacancy centers in the oxide, with $g$ close to 2.0006).

The readout scheme was proposed theoretically by Martin, Mozyrsky and Jiang (Phys. Rev. Lett. 90, 018301, 2003) and rests on energy-selective spin-to-charge conversion: the one-electron (paramagnetic) level of the trap is Zeeman-split by a static field, and the channel Fermi level is placed between the two spin components. A microwave field at the resonance frequency flips the spin; since only one spin orientation leaves the trap level available below the Fermi level, each spin flip changes whether the trap holds an electron, so the spin state is converted into a charge state and hence into the average channel current. That the trap of their device really is paramagnetic when singly charged (one unpaired electron) and becomes a spin singlet when doubly charged was established beforehand through the magnetic-field dependence of its RTS statistics (Xiao, Martin and Jiang, Phys. Rev. Lett. 91, 078301, 2003).

In the 2004 experiment the transistor (channel about 300 nm by 240 nm, near pinch-off) was held at a bath temperature of about 0.4 K and irradiated at 45.1 GHz; the resonance of the single trap appeared at a magnetic field of about 16,025 G, giving $g = 2.02 \pm 0.015$, clearly above the value $g \approx 1.998$ of the conduction electrons used as an internal reference and also above the known $P_b$ and $E'$ values. The ESR line (full width at half maximum of 5 to 10 G) corresponds, through the standard linewidth relation, to a spin-spin relaxation time $T_2$ of roughly 0.1 μs. At the microwave power used, the Rabi frequency $\gamma H_1$ (the rate at which the resonant microwave magnetic field $H_1$ rotates the spin, with $\gamma$ the gyromagnetic ratio) was about 10 kHz, comparable to the trap's measured electron tunneling rate of about 20 kHz, and in this strong-driving regime the response became nonlinear. The detection chain had a charge sensitivity of about $10^{-4}$ electrons per root hertz, and the microwave irradiation heated the electron system so that its effective temperature was about 1.5 K against the 0.4 K bath.

The experiment therefore sits at the intersection of two research directions that both remain active. One is electrically detected magnetic resonance (EDMR), the detection of electron spin resonance through spin-dependent changes of a device current rather than through inductive detection; EDMR is standard in defect spectroscopy of semiconductor devices, and its nanoscale, few-spin limit raises exactly the questions of how resonant spin flips, non-resonant microwave effects (heating and voltage pickup), and charge dynamics combine. The other is single-spin readout and control for quantum information: single-shot electrical readout of one electron spin in silicon was later achieved with phosphorus donors (Morello et al., 2010), and coherent ESR control of a single donor spin with electrically detected Rabi oscillations followed (Pla et al., 2012). Those architectures, and the double-quantum-dot ESR work to which the same UCLA group later turned (Hao et al., 2014), superseded the single-oxide-trap platform in practice, but they do not answer the mechanistic questions that the 2004 trap experiment raised. Two specific technical terms used below: power broadening is the artificial widening of a resonance line by strong driving, which shortens the apparent $T_2$; and g-tensor modulation resonance (Kato et al., 2003) drives spin transitions by modulating, with an alternating gate voltage, the orientation-dependent g-factor of a confined electron, instead of applying an oscillating magnetic field, thereby reducing the required microwave power.

Problem Statement

For the single paramagnetic trap in the gate oxide of a silicon n-channel field-effect transistor studied by Xiao, Martin, Yablonovitch and Jiang (Nature 430, 435, 2004), whose ESR was detected electrically through spin-to-charge conversion (each resonant spin flip changes whether the trap holds an electron, and hence the average channel current) read out as a random telegraph signal (the two-level random switching of the source-drain current produced by the trap capturing and emitting single channel electrons), determine the following, which the source experiment left unresolved and which the intervening literature has not settled:

(1) The mechanism of the nonlinear ESR response at high microwave power, where the Rabi frequency $\gamma H_1$ (the rate at which the resonant microwave magnetic field $H_1$, with $\gamma$ the gyromagnetic ratio, rotates the spin) of roughly 10 kHz is comparable to the trap tunneling rate of roughly 20 kHz: in this regime the spin-resonance-induced change in the trap occupancy probability inverts sign (the average source-drain current increases instead of decreasing), and the tunneling rate between the paramagnetic (singly charged, one unpaired electron) and singlet (doubly charged) charge states is modulated by up to about 10 percent at resonance. Identify the dominant mechanism, including whether the effect is a genuine nonlinear ESR phenomenon of the coupled spin-charge dynamics or is dominated by non-resonant microwave-induced changes of the trap capture and emission rates that peak at the same magnetic field, and provide a quantitative account of the observed sign inversion and rate modulation.

(2) The origin of the measured spin-spin relaxation time $T_2$ of about 0.1 μs (ESR linewidth of 5 to 10 G), which is much shorter than the roughly 25 μs typical of isolated paramagnetic centers in SiO$_2$ such as $E'$ centers in fused quartz: determine the relative contributions of the interaction of the trapped spin with the conduction electrons of the nearby channel and of microwave power broadening (the artificial widening of the resonance line, and shortening of the apparent $T_2$, caused by strong driving).

(3) The role of microwave heating, which raised the effective electron temperature to about 1.5 K against a bath at about 0.4 K and thereby limited the current sensitivity of the detection: quantify this limitation and demonstrate whether the routes the source paper proposed, g-tensor modulation resonance (driving the spin transition by modulating, with an alternating gate voltage, the orientation-dependent g-factor of the trapped electron, instead of applying an oscillating magnetic field, thereby reducing the required microwave power) or pulsed high-frequency (of order 180 GHz) sources, actually overcome it for this single-trap readout.

(4) The microscopic identity of the paramagnetic center, whose measured g-factor of $g = 2.02 \pm 0.015$ differs from the known values of $P_b$ centers (silicon dangling-bond defects at the Si/SiO$_2$ interface, g-factors around 2.003 to 2.007) and $E'$ centers (oxygen-vacancy centers in the oxide, g close to 2.0006) and from the channel-electron g-factor of about 1.998: identify the defect (or otherwise explain the g-factor), including testing or excluding the source paper's speculation of slight ferromagnetic ordering among the channel electrons.

These four questions share one scientific objective, a complete microscopic understanding of electrically detected single-electron spin resonance in a channel-coupled oxide trap, and a completion boundary recognizable by a specialist in semiconductor spin physics or electrically detected magnetic resonance: all four must be answered for the task to be resolved, each by a mechanism identification, analysis, or measurement on this physical system with an explicit quantitative account of the observed data, and answering fewer than four does not resolve the task.

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