Charge pumping through a single donor atom

Although some fascinating alternatives have been recently suggested, e.g. semiconductor quantized voltage sources (see [1]), the main task of the electrical branch of quantum metrology remains the development of reliable quantized electron pumps (QEPs) [2–12] and, as a consequence, the full implementation of the quantum metrology triangle [2]. The QEP approach to metrology was introduced in the early 1990s [4] and, since then, many interesting schemes have been proposed, each with advantages and disadvantages—see [3, 4, 6–8, 10–12]. The strong focus on QEP-based metrology is also justified by its ability to generate currents in which capture and emission processes can be controlled at the single electron level. This can be obtained by taking advantage of Coulomb blockade (CB) effects [14] as QEPs are often single electron transistor (SET) based [3, 4, 6–8, 10–13].

To be useful for metrology, a QEP needs to generate currents of the order of hundreds of pA with accuracies of 1 part in ${{10}^{8}}$ (equivalent to ${{10}^{-2}}\;{\mbox{ppm}}$). Furthermore, as the current (I) is linked to the frequency of oscillation (f) according to the simple relation ${{I}_{SD}}=fe$ [4], with e being the elementary charge, f ≳ GHz is necessary to generate the desired currents. At GHz frequencies, QEPs are known to be affected by non-adiabatic excitation errors [15, 16]. It is already understood that, to improve robustness and, as a consequence, temperature and speed of operations, their charging energy (${{E}_{C}}$) needs to be increased [17]. The ${{E}_{C}}$ is the energy that needs to be paid to a system to increase the average number of electrons it contains by one [4, 7] and, for quantum dots (QDs), is inversely proportional to its size, which makes increasing it in conventional QD-SETs a non-trivial task [18]. Between the many approaches available, the one that has been proven to be both successful and reproducible is based on single atom transistors (SATs) [19–24].

High currents and high accuracies have been recently achieved [3] in a single-parameter charge pumping configuration [10, 11] similar to the one used in this work and every possible novelty in the technology used to fabricate and to operate a QEP represents an important milestone [1, 2]. As this article will show, an isolated shallow dopant atom, due to the combination of a high ${{E}_{C}}$ and a well isolated ground state for the first electron charge state, provides, naturally, an interesting geometry for the quantum pumping of electrons. This is not the first time that dopant atoms have been used to generate pumping currents. Lansbergen et al [25] and more recently Roche et al [26] used a few dopants FET to perform pumping at MHz frequency, however, these pioneering experiments were not at the single atom level and far from the rates required for quantum metrology.

After a short introduction to the device structure, to the selection process for the location of the good devices amongst the large pool of fabricated ones and to the experimental setup in section 2, in section 3 we discuss the generation of pumped current up to GHz frequencies and we show that, for our system, it is possible to reach the ${{I}_{SD}}$ = fe quantization even for f = 1 GHz. Some considerations on the consequences of our results are discussed in section 4. In the appendix (section A.1) we give more insight into the differences between the non-adiabatic regime (studied in our experiment) and the adiabatic pumping regime. Lastly, more details on some aspects of our experiments are discussed in the appendix (sections A.2, A.3 and A.4).

The devices used in our experiments are fabricated on a complementary-metal-oxide-semiconductor (CMOS) platform [20, 27, 28] making them fully compatible with one of the most successful technologies of modern times. An adapted [27] fully depleted-silicon on insulator technology (see figure 1) is used to fabricate n-metal-oxide-semiconductor field-effect-transistors (n-MOSFETs). The 20 nm thick SOI channel is initially P doped with a background concentration of ${{10}^{18}}$ ${\mbox{c}}{{{\mbox{m}}}^{-3}}$ and then is etched to form the channel of the device which is sitting on top of a 150 nm thick buried oxide, as shown in figure 1(b). The device fabrication is then completed by using a technology similar to that used in commercial trigate SOI MOSFETs [27]. The only difference is that, in our devices, not only is one gate (polycrystalline silicon) wrapped around three sides of the channel (see figure 1(b)), but two are positioned in series (see figure 1(a)) along the direction of electron transport. Finally, to protect the channel from the high doping doses (HDDs) necessary for the formation of the source and the drain regions, 15 nm thick ${\mbox{S}}{{{\mbox{i}}}_{3}}{{{\mbox{N}}}_{4}}$ spacers (see figure 1(a)) are formed around the two gates [20] and the HDD implantation is performed at an angle of $55{}^\circ$. This configuration prohibits As dopants from the HDD from reaching the portion of the channel between the two gates. Furthermore, within this channel, the original P doping yields only a few active P atoms, which provide the ${{D}_{0}}$ states shown in figure 3, hence allowing the observation of the SAT behaviour [19–24]. Note that in our devices the P atoms are present in the centre of the channel only due to the initial background doping procedure discussed above. Furthermore, as shown in figures 2 (a) and 3, room and low temperature [20, 28] electrical characterization can be used to study the presence of this discrete number of isolated dopants in the channel and their effects on the transport characteristics.

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The low temperature measurements were performed by mounting the device on a stage that is dipped directly in liquid helium and thus at 4.2 K. A low noise battery operated measurement setup (see [29–31]) was used to measure the source/drain current and to apply the voltages. As the amplifier is at room temperature, the absolute noise floor of the IV-converter is limited by the Johnson noise of the feedback resistor, which is given by $\sqrt{\frac{4{{k}_{B}}T}{{{R}_{f}}}}=4\frac{{\mbox{fA}}}{\sqrt{{\mbox{Hz}}}}$. To apply the sinusoidal RF input to one gate an Agilent 8648C source was used. An important aspect of our setup is that a cryogenic bias-T [3], in red in the circuit schematic of figure 1(a) and 1(b), is used to add this RF voltage to one of the two DC voltages applied to both the gates; this in a single-parameter charge pumping configuration [3, 10, 11].

Our double gate (TG1 and TG2 in figure 1(a)) configuration allows the control of both the left and the right barriers, thereby confining the electrons into the atomic potential using an approach similar to the one recently implemented elsewhere [3, 7, 10, 11]. However, differently from previous methods [3, 7, 11], in our approach each gate is capacitively coupled with the dopant state (in a way similar to that of the global top gate used in [10] or of the back gate (BG) in [12]) and, to some extent, can also cross-couple to the barrier under the opposite gate, e.g. see schematic in figures 2(b) and 4 (b). This makes it possible to observe a pumping behaviour not previously observed in conventional pumps. As an example, in our devices the distinction between 'entrance' and 'exit' gates is not as sharp as in conventional QEPs [3, 11], which explains why both the gates can be used for the evaluation of the quantization (pumping) effects.

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Two QEPs, i.e. devices A and B, structurally similar to the one shown in figure 1(a) and figure 1(b) and having channel widths (Ws) equal to 60 nm and 800 nm and gate lengths (${{L}_{g}}{\mbox{s}}$) equal to 50 nm and 20 nm, respectively, have been selected between the many available and studied at 4.2 K.

Initially, many devices are measured at room temperature. Source-drain current versus TG1 (TG2) traces are acquired by keeping the other gate, TG2 (TG1), grounded as shown in figure 2. The following signatures (e.g. see figure 2) are used to select the good devices amongst the large pool of fabricated ones [20, 28]:

• (1)  
  Negative threshold voltages, ${{V}_{th}}$ ≲ 0 mV, indicating the dominance by a discrete number of dopant atoms in the sub-threshold region of transport [28].
• (2)  
  Almost symmetric behaviour of the gates (indicating a good control of the channel by both the gates) and good results in the lithography of the poly-gates themselves.
• (3)  
  The capability that each gate has, independently from the other, to control the channel (and to turn the transistor to the ON-state). This, at low temperature, results in the important feature that each gate can, to some extent, have some cross-coupling with the barrier under the opposite gate (as schematically shown in figure 2(b)).

The data in figure 2(a) are related to the room temperature characterization of device A studied in the main part of the manuscript, a similar selection process has been followed for device B. The data in figure 3 are related to 4.2 K characterization of device A. For devices having the distance between the two top gates (${{S}_{gg}}$) = 50 nm, such as device A and device B, only for ${{V}_{TG1}}$ and ${{V}_{TG2}}$ ≳100 mV can artificial atom systems (i.e. QDs) be induced under the two top gates. Therefore, the sub-threshold (for ${{V}_{TG1}}$ and ${{V}_{TG2}}$ ≲ 100 mV) current signature can only be dopant related, see also similar results in [20, 25, 26, 28]. Figure 3 indicates that our approach enables the few electrons regime [20] to be accessed and gives a first indication of the fact that, for device A, the first charge state (${{D}^{0}}$) of a single isolated P dopant atom (located in the central region of the channel) is addressed. As our pumping approach requires low transparency of the tunnel barriers, the exact quantification of the ${{E}_{C}}$ in the CB diamonds of figure 3(a) is not straightforward. The estimation of ${{E}_{C}}$ ≈ 35 meV obtained in this figure 3(a), however, was confirmed in the strong coupling regime [24] measurements of figure 3(b). This strong coupling regime is not optimal for pumping but it allows the observation of the CB diamond for a gate position similar to the one where it is only partially visible in figure 3(a).

These results agree with the analysis of the AC data discussed in section 3 and with recent observations by other groups [20, 25, 26, 28]. Furthermore, for our pumping experiments, the channel thicknesses (T) and ${{S}_{gg}}$ have always been fixed at 20 nm and 50 nm respectively because, unlike W and ${{L}_{g}}$, the parameter ${{S}_{gg}}$ has proven to be important. As an example, the absence of transport in the sub-threshold region and a regular double quantum dot (DQD) signature [32] in the region of inversion, i.e. for ${{V}_{TG}}$ʼs ≳100 mV, have been observed for other measured devices having ${{S}_{gg}}$ $>$ 50 nm (see section A.2). These facts are an indication of the absence of transport through isolated dopants and indeed pumping through isolated dopants has proved not to be possible in this latter case.

We can now turn to the RF measurements of device A. In figures 4, 5, 6 and 7, the data related to the generation of pumping currents when a sinusoidal voltage excitation, ${{V}_{RF}}$, is provided to TG2 are shown. The asterisk, '*', used for the AC data, indicates for each pump which of two gates is excited by RF oscillations. Taking advantage of the knowledge gained in the DC transport experiments illustrated in figure 3, the top gates are tuned to values far from the ones of the DC transport regime, i.e. in the region indicated with the red star in figure 3(a). For these voltage values, transport can only be related to the transiting of electrons through the atom-dot following the pumping scheme introduced in figure 1(c). This is also illustrated in figure 4(c), where the reaching of unity steps proportional to the frequencies of excitation, f, ranging from 25 MHz to 1 GHz and the subsequent following of the expected ${{I}_{SD}}$ = fe law are shown. Furthermore, in our pumps, the sign of the current does not depend on the sign of ${{V}_{SD}}$ but on which gate is selected to be RF excited [10, 33], i.e. the data of figure 8 related to device B have been acquired by using ${{V}_{SD}}=-2$ mV. The independence of the current from the source/drain polarity is another strong indication of the pumping nature of a current [10]. These last facts allow us to illustrate some of the great advantages of our SAT based single-parameter configuration, which, by combining an isolated ground state with large ${{E}_{C}}$ʼs, allows the extension of the non-adiabatic pumping regime [10, 11, 34] for at least three orders of magnitude, i.e. from the MHz to the GHz regime of operations. This also occurs since a careful control of the phase of the excitation is not necessary [10].

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As shown below, the analysis of the triangular shape observed in figure 4(a) (and in figures 5 and 6) brings further evidence that the pumping signature studied for device A is dopant related. In region III, the ac transport is never possible. In region I, opposite to angle β, the current is limited because the electrons are blocked at the entrance of the pump (stage 1 in figure 1(c)). This is true unless TG1 can compensate for the lack of action of TG2 in addressing the barrier under it and the state [35]. This also justifies the association between β and the value of coupling between TG1 and the state and the value of the cross-coupling between TG1 and the barrier under TG2, see figure 4(b) for a schematic. The estimated value for β (the voltage ratio $\frac{\vartriangle {{{\mbox{V}}}_{TG1}}}{\vartriangle {{{\mbox{V}}}_{TG2}}{{|}_{{\mbox{I}}}}}={\rm tan} \beta$ is ≈ 8.5, hence β ≅ 83.3°) indicates that the black dotted onset line is 6.7°more tilted in the anti-clockwise direction compared to the case of having the state coupled only to TG2 and no cross-coupling between TG1 and the barrier under TG2, i.e. this case should lead to β = 90° [35]. To clarify this aspect we can see if the observed dependence of β to f agrees with it. It should be noted that expected $\beta \left( f \right)$ can be extrapolated, and so as to observe full quantization, the entrance rate (${{\Gamma }_{in}}$ in figure 4(b) in the first half of the cycle must be large compared to f [35]. So if the value of f increases, β is expected to increase, i.e.: it becomes more difficult for TG1 to be effective in correcting the lack of action of TG2 in lowering the barrier. This occurrence is demonstrated in figure 5, where it is demonstrated that the angle β increases following an increase of f. Indeed, being ${\rm tan} \left[ \beta \left( f=250\;{\mbox{MHz}} \right) \right]$ = 6.5 and ${\rm tan} \left[ \beta \left( f=1\;{\mbox{GHz}} \right) \right]$ = 8.5, we have $\beta \left( f=250\;{\mbox{MHz}} \right)$ = 81.2° and $\beta \left( f=1\;{\mbox{GHz}} \right)$ = 83.3°.

In region II, opposite to angle α, the pumping current is limited when the electrons are blocked at the exit of the pump (stage 3 in figure 1(c)). This happens because during each cycle the barrier under TG2 is so low that TG1 needs to be larger than previously to let the electrons leave the atom to the drain, see figure 4(b). When the dc value of ${{V}_{TG2}}$ decreases, the exit of the electrons and the complete cycle are facilitated and become possible for lower values of ${{V}_{TG1}}$. This justifies the association between α and the value of the coupling present between TG2 and the state and the value of the cross-coupling between TG2 and the barrier under TG1. The value for α (the voltage ratio $\frac{\vartriangle {{{\mbox{V}}}_{TG2}}}{\vartriangle {{{\mbox{V}}}_{TG1}}}{{|}_{{\mbox{II}}}}$ = ${\rm tan} \left( 90-\alpha \right)$ is ≈ 1.69, hence α is ≅ 31°) is non-zero α and β can only provide an insight into the complicated coupling and cross-coupling effects present in our system (see figure 2(b)), however, there is an important piece of information that can be extracted from these: the two voltage ratios associated with α and β are of the same order of magnitude and hence the position of the state can be inferred somewhere at the centre of the channel.

Lastly, the strong frequency dependence of the angles α and β observed in figure 5 could also be related to the capacitive coupling between the gates, as schematically shown in figure 2(b). This is because, during RF measurements, the 'fixed' gate ${{V}_{TG1}}$ will oscillate due to stray coupling with the driven gate ${{V}_{TG2}}$ and the amplitude and the phase of this parasitic oscillation will be frequency dependent.

By following the black and red dashed lines towards more negative values of ${{V}_{TG1}}$ it is possible to observe that they do cross (the red star in figures 4(a) and 5). In conventional electron pumps [3, 11, 33, 35], the confinement site is created by applying negative voltages to gates above a two-dimensional electron gas (2-DEG) and the energy state of the QD is completely manipulated by the barriers and crosses the Fermi level when the barriers are already transparent enough to observe pumping current [35]. Moreover, the state used for pumping is localized in a region that comprises many atomic sites and as a consequence, for these 2-DEG induced QDs [3, 11, 35], there is always a certain range of ${{V}_{TG1}}$ and ${{V}_{TG2}}$ where the onset of the pumping transport can be observed (i.e. the shape of the plateau in the 2D stability is trapezoidal and not triangular). This observation reflects the fact that for these confining potentials the states are not strongly localized and can tolerate some deformation from the gates before transiting from one regime to another. However, when the localization of the state is increased, for example following the application of a magnetic field perpendicular to the plane [3, 11, 33], a drastic reduction of this range of tolerance is observed. Indeed, as shown in figure 2 of [11], the trapezoidal shape of the 2D stability approaches the triangular one with the application of a magnetic field.

The fact that in our system this region of tolerance is reduced to a small region of the 2D stability (red star in figures 4(a) and 5), even without the presence of a magnetic field, indicates that the potential confining the electrons is localized in a few atomic sites, i.e. is related to an isolated donor atom [19] and not a QD. This occurs because, for an atom pump, the barriers are not transparent enough when the state crosses the Fermi level (as also seen in figure 3(a)), and the crossing line is only seen for the second electron (outlined by the black circle in figure 4(a)). Furthermore, as shown in figure 6 for f = 250 MHz, following an increase of the RF power (PW) from $-7.5$ dBm to $-5.5$ dBm, the triangular shape equivalent to the one observed in 4(a) does not seem to be dramatically deformed but just shifted towards more negative gate voltage values. This last observation is dramatically different from the ones attributed to conventional QEPs, see [3, 11, 35] and references therein. This is again in agreement with the idea that a strong local potential, having a shape less affected by the gates if compared to conventional QEPs, is responsible for the confinement of our pumping electrons, so that the increase of PW can move the onset of the pumping current to the more negative of the DC gate voltages. Lastly, the second plateau observed in figure 4(a) (black circle) can be associated with the 2e state (${{D}^{-}}\;{\mbox{state}}$ [36]) of the first atom or with the 1e state of a second atom. For this reason, in this paper, we only study the first quantization step.

To conclude the discussion on device A, figure 7 shows the data for the RF currents and the derivative of the currents for different frequencies. From the data of figure 7 it is possible to extrapolate that, in our system, the onset of the pumping current starts to be mildly affected by non-adiabatic excitations [15, 33] only for ${{f}_{SAT}}$ ≈ 1 GHz and, as also shown in figure 4, little degradation of the quantization is observed even for this range of frequencies. If we compare this ${{f}_{SAT}}$ to the onset of non-adiabatic excitations observed in QD-QEPs [15, 33], i.e. ${{f}_{QD}}$ ≈ 200 MHz, we have another indication of the fact that the system addressed in our experiments is characterized by higher energies if compared to conventional QEPs. Indeed, for a SAT [20], all the energy scales (e.g. ${{E}_{C}}$ ≈ 30–40 meV and $\Delta {{E}_{{\mbox{Atom}}}}$ = ${{E}_{1}}$-${{E}_{GS}}$ ≈ 10 meV, with ${{E}_{GS}}$ being the ground state and ${{E}_{1}}$ the first excited state) are higher if compared to those of a QD-QEP [15, 33] and it is therefore possible to observe charge pump quantization at 1 GHz. Plus, even if our SAT pumps are operating at relatively high temperatures (${{T}_{op}}$ $=$ 4.2 K), as the condition ${\rm exp} \left( -\frac{{{E}_{C}}}{{{k}_{B}}{{T}_{op}}} \right)$ ∼ 0 is still holding, thermal errors [37] can be ignored. In conclusion, in our SAT system, high ${{E}_{C}}$ (i.e. immunity to thermal effects) combined with the isolated ground state (i.e. immunity to non-adiabatic excitations) allows the observation of the quantized non-adiabatic regime [34] for a wide range of frequencies. This is telling us that the use of SAT systems [19, 20, 22] having larger ${{E}_{C}}$ and larger $\Delta {{E}_{{\mbox{Atom}}}}\;{\mbox{signatures}}$, if compared to those associated with the present system, could allow further improvements of the pumping performances.

From the data of device B, selected and characterized via room and low temperature DC measurements identical to device A, we gain a more precise idea of the robustness of our SAT approach. As the setup used in our experiments is a state-of-the-art custom build ultra low noise apparatus [29–31], it is able to provide a noise floor of $\frac{4\;{\mbox{fA}}}{\sqrt{{\mbox{Hz}}}}$ when a 1 G $\Omega$ feedback resistor is used in the amplification and $\frac{12\;{\mbox{fA}}}{\sqrt{{\mbox{Hz}}}}$ when a 0.1 G $\Omega$ feedback resistor is used (as for all our data). Hence, in this configuration, a 10 Hz bandwidth will lead to the association of 40 fA of error to each point. Furthermore, the current data of this figure 8(b) has been obtained by repeating the same 10 Hz bandwidth trace ≈ 1200 times in 24 h and therefore the effective bandwidth could be as low as $\frac{10\;{\mbox{Hz}}}{\sqrt{1200}}$. However, the optimal bandwidth was estimated by also taking into account the long time instabilities associated with our room temperature acquisition system. In the case of the current data of figure 8(b), the optimal trade-off leads to a bandwidth around 1.6 Hz and to an estimated error of around 15 fA for each point in the plateau. Indeed, a standard error of the mean of this order of magnitude has also been extracted from the data in the plateau region of this figure 8(b). These facts give an indication on the robustness and on the reproducibility that can be associated with our system. Furthermore, the data of figure 8 are important as they demonstrate that we can obtain the ${{I}_{SD}}$ = fe quantization for f = 1 GHz in two different devices.

The results presented in this paper link pumping of electrons in a single-parameter configuration to the first charge state of a single isolated atomic potential. Although the SAT approach to QEP shows some differences from approaches based on conventional pumps, as an atom provides an isolated ground state with high ${{E}_{C}},$ this system appears to be a promising QEP geometry. The fact that the fe quantization can be observed in two different devices, even when the gate oscillates at 1 GHz, is of interest as it was obtained at 4.2 K, without the need for a high magnetic field to increase confinement and specifically designed cycles to avoid dramatic non-adiabatic excitations. Furthermore, this result aligns with requests by the most recent theoretical proposals [38] and indicates that the atom potential naturally provides a good charge pumping system.

In our work, we not only demonstrated the single atom limit of pumping in a CMOS compatible device, but also the validity of earlier theoretical predictions [7, 17] linking high ${{E}_{C}}$ʼs with high f of operations. The simplicity of our approach, requiring only liquid helium temperatures, should allow easy scaling to the more complicated devices recently suggested for error correction [38]. As there is a large research effort in the direction of the fabrication of SATs [19, 20, 22, 23], progress could be rapid. In conclusion, this work demonstrates that an isolated dopant atom is not only a promising platform to build a quantum computer [23], but also for QEPs.

The devices used in this work have been designed and fabricated in the AFSiD Project, see http://www.afsid.eu. The authors thank K Beckmann for his help during the initial phases of the experiments and A Rossi, M Governale and L C L Hollenberg for some useful discussions during the preparation of this manuscript. G C Tettamanzi acknowledges financial support from the ARC-Discovery Early Career Research Award (ARC-DECRA) scheme, project title: Single Atom Based Quantum Metrology and ID: DE120100702 and from the UNSW under the GOLDSTAR Award 2013 scheme. S Rogge acknowledges the ARC FT scheme, project ID: FT100100589.

A.1. On the non-adiabatic pumping regime of our RF data

A.2. More details on the device selection process

In fact, as the data in figure A.1 show, the 2D current diagram for a device very similar to devices A and B but having ${{S}_{gg}}$ = 70 nm, e.g. larger than 50 nm, the DQD signature is present while the dopant-atom signature, especially in the sub-threshold regions of transport, is substantially suppressed. Indeed, in this figure A.1(b), the complete lack of transport for ${{V}_{TG1}}$, ${{V}_{TG2}}$ ≲ 100 mV is observed even when (not shown in the figure A.1) a large source/drain bias is applied. Furthermore, the absence of dopant related signature is also observable in the ${{V}_{TG1}}$, ${{V}_{TG2}}$ ≳100 mV region of figure A.1(a), i.e. in the DQD region related to the two top gates, as a regular honey-comb structure [32] is observed.

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Lastly, if the states observed for ${{V}_{TG1}}$, ${{V}_{TG2}}$ ≲ 100 mV in figure 3 of the main manuscript were related to a QD formed in the centre of the channel and not to dopants, a change of ${{S}_{gg}}$ of 20 nm could (slightly) influence their ${{E}_{C}}$ but would not be sufficient to shift their position of ≈ 0.2 V. These facts are an indication of the absence of transport through isolated dopants and indeed pumping through isolated dopants has proved not to be possible in this latter case.

A.3. Current plateaus at different frequencies

In figure A.2 the evolution of the pumping currents for device A and for the different f are shown.

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A.4. More details on the analysis used for device B