Control of the ionization state of three single donor atoms in silicon

By varying the front-gate and the substrate voltages in a short silicon-on-insulator trigate field-effect transistor, we control the ionization state of three arsenic donors. We obtain good quantitative agreement between three-dimensional electrostatic simulations and experiment for the control voltages at which the ionization takes place. It allows us to observe the three doubly occupied states As${}^{-}$ at strong electric field in the presence of nearby source-drain electrodes.

Figure 1

(a),(b) Schematic cross-sectional view of the device. Vertical cut along the transverse $z$-$y$ plane (a) and horizontal cut along the $x$-$y$ plane (b). (c) Color plot of the source-drain linear conductance vs back- and front-gate voltages ($V_b$ and $V_g$, respectively) at $T=4.2$ K. The blue dashed line is the simulated threshold voltage assailing no donors in the channel. The three pairs of DILs, denoted by $A$-$A^{\prime }$, $B$-$B^{\prime }$, and $C$-$C^{\prime }$, are found in the subthreshold regime. They correspond to the ${\text{As}}^{+}$/${\text{As}}^0$ and ${\text{As}}^0$/${\text{As}}^{-}$ transitions of three As donors. The ionization states ($a,b,c$) for the three donors are indicated between the DILs ($a$, $b$, and $c$ can be 0, 1, or 2 depending on whether the corresponding donor is empty, singly, or doubly occupied, respectively). States with more than four electrons on the three donors are barely visible because of the strong coupling with the conduction band. According to our simulation the donor corresponding to the $C$-$C^{\prime }$ pair of DILs is closer to the front gate, while the other two donors are closer to the BOX. The black line is the simulated DIL for a donor located at $(x,y,z)=(0,15,\text{and}3\text{nm})$. Inset: Zoom-in of the crossing between the $A$ and $C$ DIL at $T=1$ K showing a weak Coulomb repulsion.

Figure 2

Calculated DILs in the ($V_b,V_g$) plane for a three-donor configuration. (a) The donors differ by their $x$ position ($x,y=15$ nm, $z=3$ nm) as sketched in the inset: $x=0$ (respectively, 3, $-$5) for the donor represented in black (respectively, blue, red), keeping a constant distance to the gates. (b) The donors differ by their $z$ [($x=0$, $y=15$, $z=\left\{3\right(\text{black}),7.5(\text{blue}),12(\text{red}\left)\right\}$), full lines], as sketched in the inset, or $y$ [($x=0,y=\left\{15\right(\text{black}),20(\text{blue}),23(\text{red}\left)\right\},z=3$), dashed lines] position. Both cases correspond to varying the distance to the front gate. For all simulations, the black donor is at the same position as the simulated one in Fig. 1.

Figure 3

Color plot of the S-D differential conductance at $T=4.2$ K and $V_b=10$ V. The observed resonances correspond to DILs $A$ and $A^{\prime }$. The Coulomb-blockade regimes associated with the ${\text{As}}^{+}$, ${\text{As}}^0$, and ${\text{As}}^{-}$ charge states are indicated. As expected, the lever arm factor is smaller for $A^{\prime }$ than for $A$ (see text). The lines of differential conductance appearing at finite $V_d$ and parallel to the diamond are due to fluctuations in the local density of states of the S-D extensions [3]. They present approximately the same pattern for $A$ and $A^{\prime }$, but they are more blurred for $A^{\prime }$ due to the larger tunnel coupling.