Spin-dependent processes at the crystalline ${\text{Si-SiO}}_2$ interface at high magnetic fields

An experimental study on the nature of spin-dependent excess charge-carrier transitions at the interface between (111)-oriented phosphorous-doped $\left(\left[\text{P}\right]\approx {10}^{15}{\text{cm}}^{-3}\right)$ crystalline silicon and silicon dioxide at high magnetic field $\left(B_0\approx 8.5\text{T}\right)$ is presented. Electrically detected magnetic-resonance (EDMR) spectra of the hyperfine split ${}^{31}\mathrm{P}$ donor-electron transitions and paramagnetic interface defects were conducted at temperatures in the range of $3\text{K}\le T\le 12\text{K}$. The results at these previously unattained (for EDMR) magnetic-field strengths reveal the dominance of spin-dependent processes that differ from the previously well investigated recombination between the ${}^{31}\mathrm{P}$ donor and the $P_b$ state, which dominates at low magnetic fields. While magnetic resonant current responses due to ${}^{31}\mathrm{P}$ and $P_b$ states are still present, they do not correlate and only the $P_b$ contribution can be associated with an interface process due to spin-dependent tunneling between energetically and physically adjacent $P_b$ states. This work provides an experimental demonstration of spin-dependent tunneling between physically adjacent and identical electronic states as proposed by Kane [Nature (London) 393, 133 (1998)] for readout of donor qubits.

Figure 1

A sketch of the sample used in these experiments. The sample is fabricated on Si(111) doped with ${10}^{15}$ phosphorus $\text{donors}/{\text{cm}}^3$. Contacts are made to the sample using aluminum contacts and the surface is covered with a native ${\text{SiO}}_2$ layer. A simple measurement circuit is also shown. The sketch is not to scale, although the indicated dimensions are accurate.

Figure 2

(Color online) (a) Plots of the relative photocurrent changes as a function of the applied magnetic field $B_0$ at temperatures $T=3$, 6, and 12 K. The data were taken with a photocurrent $I=600\text{nA}$. The signal was obtained by microwave chopping ($500\mu \text{s}$ pulse length, 1 kHz shot repetition rate) and lock-in detection of the photocurrent. (b) Plots of the photocurrent changes as a function of time following a microwave pulse with ${\tau }_p=8\mu \text{s}$ length for magnetic fields off resonance, on resonance with the low-field ${}^{31}\mathrm{P}$ peak, and on resonance with the $P_b$ peak at $T=12\text{K}$. The data were collected from the average of many transients measured with a 1 kHz shot repetition rate.

Figure 3

Plot of the integrated area $A$ under each of the three resonances as a function of the temperature. The linear fit to the $P_b$ data between 3 and 10 K shows excellent agreement. The data at $T=12\text{K}$ were taken at a different illumination intensity. The line joining the data for the ${}^{31}\mathrm{P}$ resonances is a guide to the eye.

Figure 4

(a) Cartoon of spin-dependent tunneling between two adjacent uncharged $P_b$ centers where the ground-state energy of one $P_b$ matches the $P_b^{-}/P_b$ charging energy of the other. (i) Initially, the pair is in a triplet state and tunneling is not possible. (ii) Once the spin of one $P_b$ state is changed the pair has singlet content and tunneling (iii) is allowed. (iv) An excess charge-carrier pair recombines as it discharges the two charged $P_b$ states. (b) Sketch of DOS of $P_b$ centers within the $c\text{-Si}$ band gap (Ref. 5). Note that DOS’s of $P_b$ and $P_b^{-}$ are assumed to be identical but shifted by the correlation energy $\Delta$. (c) Plot for $T=10\text{K}$ of the number of (i) filled $P_b$ states, (ii) filled $P_b^{-}$ states, and (iii) tunneling pairs as a function of energy about the quasi-Fermi level $E_{\text{QF}}$. The sharper pair distribution for $T=5\text{K}$ is indicated by the solid line. The plot illustrates that there are fewer pairs of adjacent $P_b$ and $P_b^{-}$ with matching energies when $T$ decreases.