Isolation and manipulation of a single-donor detector in a silicon quantum dot

We demonstrate the isolation and electrostatic control of a single phosphorus donor in a silicon quantum dot by making use of source-drain bias during cooldown and biases applied to capacitively coupled gates. Characterization of the device at low temperatures and in magnetic fields shows single donors can be electrostatically isolated near one of the quantum dot's tunnel barriers with either single or double occupancy. This model is well supported by capacitance-based simulations. The ability to use the ${\mathrm{D}}^0$ state of such isolated donors as a charge detector is demonstrated by observing the charge stability diagram of a nearby and capacitively coupled semiconnected double quantum dot.

Figure 1

(a) SEM image of the device used in the experiments with the quantum dot connected to source and drain leads (QD, bottom) as well as the semiconnected double quantum dot (SDQD, top) with its capacitively coupled gate $V_1$ and tunnel-coupled gate $V_2$. (b) Transverse structure of the device across A-B. (c) Energy profile along C-D at low temperatures when the cooldown is performed without biasing (all connections grounded), (d) energy profile at intermediate temperatures for a biased cooldown, and (e) at low temperatures after the creation of the electrostatic tunnel barrier isolating the donor.

Figure 2

Variation of the conductivity in temperature showing a screened correlated hopping conduction mechanism,e.g., $\mathrm{\Delta }\sigma \propto \exp (-{(T_{\mathrm{ES}}/T)}^{1/2})$, where $T_{\mathrm{ES}}$ is a characteristic temperature. Inset shows the variation of the applied source-drain bias during cooldown with $V_{\mathrm{SD}}\gg E_{\mathrm{C}}$, with $E_{\mathrm{C}}$ the quantum dot charging energy. The $T^{-1/2}$ law demonstrates the presence of electron-electron interaction in an insulating system compatible with $R>{\lambda }_{\mathrm{TF}}^{-1}$ with ${\lambda }_{\mathrm{TF}}^{-1}$ the Thomas-Fermi screening length and $R$ the hopping length [27, 28].

Figure 3

(a) Amplitude of the differential current showing coulomb diamonds at 300 mK following a cooldown under the strong bias condition. (b) Detailed region of (a) around the ${\mathrm{D}}^{+}-{\mathrm{D}}^0$ state transition (white box), showing fine features resulting from the main quantum dot, (c) Coulomb diamonds at 300 mK following a cooldown under normal conditions, e.g., all contacts grounded, showing the SET operating as a single quantum dot.

Figure 4

Displacement in $V_{\mathrm{SD}}$ and $V_{\mathrm{g}}$ of a typical feature (white star) at the ${\mathrm{D}}_{+}-{\mathrm{D}}_0$ transition as a function of the magnetic field applied perpendicularly to the device.

Figure 5

(a) Capacitance model for a semiconnected double quantum dot and its charge detector represented here in its simplified version by a single electron transistor. (b) Closer view of (a) (white box) of the capacitance associated with the active donor D1. (c) Schematics of the energy levels and tunneling processes involving the two donors. Tunneling from and to the drain contact and the SET are allowed via D1. However, due to the energy difference, such a process is not allowed in D2 which can only be charged and discharged via the drain.

Figure 6

(a) Simulated Coulomb diamonds showing, the ${\mathrm{D}}^{+}$, ${\mathrm{D}}^0$ and ${\mathrm{D}}^{-}$ with shifts induced by the presence of the second impurity in the tunnel barrier. (b) Details at the edge of the diamond showing the effect on the quantum dot when in series with the donor [white box area in (a)]. (c) Simulation of the Coulomb diamonds in the unbiased cooldown case, e.g., in the absence of donors in the barrier.

Figure 7

(a) Compensated charge stability diagram for the SDQD at 300 mK. (b) Current profile along $V_1$ showing individual electron tunneling event inside the double dot. (c) Current profile at the bi-stable region involving tunneling events from individual dots to the gate $V_2$. (d) Current profile along $V_2$ indicating electrons tunneling out of the double dot into the gate reservoir.