Spin-Polarized Transient Electron Trapping in Phosphorus-Doped Silicon

Experimental evidence of electron spin precession during travel through the phosphorus-doped Si channel of an all-electrical device simultaneously indicates two distinct processes: (i) short time scales ($\approx 50\mathrm{ps}$) due to purely conduction-band transport from injector to detector and (ii) long time scales ($\approx 1\mathrm{ns}$) originating from delays associated with capture or reemission in shallow impurity traps. The origin of this phenomenon, examined via temperature, voltage, and electron density dependence measurements, is established by means of a comparison to a numerical model and is shown to reveal the participation of metastable excited states in the phosphorus-impurity spectrum. This work therefore demonstrates the potential to make the study of macroscopic spin transport relevant to the quantum regime of individual spin interactions with impurities as envisioned for quantum information applications.

Figure 1

(a) Schematic band diagram of vertical $n$-type doped Si spin transport channel devices used in this work, showing band bending and the resultant potential minimum for temperatures high enough to ionize dopants and low applied voltage $V_{C1}$. (b) Illustration of the model implied by Eq. (1) for capture of electrons (incident with period ${\tau }_i$) by one of $N$ shallow traps $\Delta E$ below the conduction band with probability $\alpha$. Each trap is initially empty with probability $P_E$ and releases the electron with an exponential probability distribution having time scale ${\tau }_t$.

Figure 2

Perpendicular-field measurements at 55 K. (a) A full field loop displays square hysteresis and clear low-field dephasing. (b) Voltage dependence of the low-field signal is shown, where the applied voltage $V_{C1}$ is changed from 0, 0.5, 1.0, and 1.5 to 2.5 V in steps of 0.1 V.

Figure 3

Temperature dependence of low-field dephasing between 40 and 100 K at applied voltage $V_{C1}=1.5\mathrm{V}$. (b) Simulated spin-precession Hanle signals using the trapping-time model [Eq. (1)] with parameters $\alpha =0.2$, ${\tau }_0=200\mathrm{ps}$, $\Delta E=11.5\mathrm{meV}$, and effective 1D current of 3 nA sampling $N=50$ traps. Inset: Calculated trapping-time distributions.

Figure 4

Low-field dephasing as a function of injected current and hence steady-state electron density. In (a) spin polarization is shown, whereas (b) demonstrates a reduction in the relative contribution to the overall signal from trapped electrons when density increases. Our numerical model included for comparison uses an effective one-dimensional current.