Transport spectroscopy of coupled donors in silicon nano-transistors

The impact of dopant atoms in transistor functionality has significantly changed over the past few decades. In downscaled transistors, discrete dopants with uncontrolled positions and number induce fluctuations in device operation. On the other hand, by gaining access to tunneling through individual dopants, a new type of devices is developed: dopant-atom-based transistors. So far, most studies report transport through dopants randomly located in the channel. However, for practical applications, it is critical to control the location of the donors with simple techniques. Here, we fabricate silicon transistors with selectively nanoscale-doped channels using nano-lithography and thermal-diffusion doping processes. Coupled phosphorus donors form a quantum dot with the ground state split into a number of levels practically equal to the number of coupled donors, when the number of donors is small. Tunneling-transport spectroscopy reveals fine features which can be correlated with the different numbers of donors inside the quantum dot, as also suggested by first-principles simulation results.


Stability diagrams for selectively-doped SOI-FETs (device C)
A usual procedure to identify the origin of the fine features (e.g., inflections) in current peaks due to tunneling transport through a QD is to measure and analyze the stability diagrams, i.e., plots of ID versus VG and VD. [1][2][3] Such analysis has also been applied to characterize individual donors working as QDs in silicon devices. [4][5][6] In such diagrams, it is usual to observe zero-current stable-charge regions (Coulomb diamonds) as signatures of Coulomb blockade transport mechanism.
For device C shown in the manuscript, we measured the stability diagrams for a VG range corresponding to the first two current peak envelopes, as shown in Figs. S1a and S1b. In the VG-VD space, absolute value of ID [abs(ID)] is plotted; this allows us to show the contour plot in a logarithmic color scale. Since the peak envelopes are affected by relatively large background diffusion current, the fine features are rapidly masked as VD increases. Different cutoff-current levels are, therefore, used in Figs. S1a and S1b in order to emphasize features appearing around the first and the second current peak envelope, respectively.
First of all, as delineated by solid lines, distinct Coulomb diamonds can be identified (around VG~1.6 V and ~1.8 V, respectively). These diamonds can be basically ascribed to consecutive stable charge states of a single QD. The diamonds appear slightly separated from each other in VG, which seems to be inconsistent with classical Coulomb blockade theory for a QD.
However, it should be noted that the background diffusion current is continuously increasing after the onset and this induces some distortion in the Coulomb diamonds. In the model of a single QD, it is reasonable to ascribe the features (inflections) observed within the current regions, i.e., between the Coulomb diamonds, to transport influenced by the discrete energy levels of this QD.
Dashed lines are drawn as simple guides to illustrate the expected behavior of such features. Because of the superimposed background diffusion current, the fine features embedded in the peak envelopes become quickly blurred as VD is increased, which hinders their detailed analysis. Despite the blurring and difficulty in analysis of the fine features, the observed Coulomb diamonds (Fig. S1a and S1b) are in reasonably good agreement with our interpretation.
In Figs. S1c and S1d, we also show the transconductance, dID/dVG. In principle, such a plot should emphasize more clearly the fine features, but, since the large diffusion current increases the background current, transconductance is also significantly affected. However, some traces running vertically in these diagrams, i.e., weakly dependent on VD, are faintly seen. Such features may be related to multi-QD tunneling 7 , but further experimental study is needed to fully clarify this behavior in our devices.
We also plot a few ID-VG curves for negative VD's (in Fig. S1e) and for positive VD's (in Fig. S1f) along the dotted lines indicated in Figs. S1a and S1b. The features embedded in the peak envelopes can be thus correlated with the features observed within the stability diagrams.
Considering the above data, the most likely origin of the features observed in the current peak envelopes is transport through the energy states of a QD located in the device channel, as also described in the manuscript. However, more complex "multi-tunneling" transport through multi-QDs cannot be completely excluded.
Finally, since the slopes of the stable-charge region (Coulomb blockade) boundaries can be associated with the capacitive coupling of the QD to source, drain, and gate, it is possible to extract the lever-arm factor, α, defined as α = dEQD/dVG (eV/V), i.e., the fraction of VG used to modify the energy within the QD (EQD). For device C, after analyzing these boundaries (delineated by solid lines in Fig. S1), α is found to be 0.09±0.01 eV/V. This value is used to estimate the energy spacing between consecutive energy levels within the QD, as discussed in the manuscript.