Home
Search
Collections
Journals
About
Contact us
My IOPscience
The coupled atom transistor
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 J. Phys.: Condens. Matter 27 154206 (http://iopscience.iop.org/0953-8984/27/15/154206) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 169.230.243.252 This content was downloaded on 24/03/2015 at 07:34
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 154206 (8pp)
doi:10.1088/0953-8984/27/15/154206
The coupled atom transistor X Jehl1 , B Voisin1 , B Roche1 , E Dupont-Ferrier1 , S De Franceschi1 , 2 ´ , O Cueto2 , M Sanquer1 , M Cobian1 , Y-M Niquet1 , B Sklenard 2 2 R Wacquez and M Vinet 1 University Grenoble Alpes, INAC, F-38000 Grenoble, France and CEA, INAC-SPSMS, F-38054 Grenoble, France 2 University Grenoble Alpes, LETI, F-38000 Grenoble, France and CEA, LETI, Minatec campus, F-38054 Grenoble, France
E-mail: [email protected] Received 30 July 2014, revised 20 January 2015 Accepted for publication 22 January 2015 Published 18 March 2015 Abstract
We describe the first implementation of a coupled atom transistor where two shallow donors (P or As) are implanted in a nanoscale silicon nanowire and their electronic levels are controlled with three gate voltages. Transport spectroscopy through these donors placed in series is performed both at zero and microwave frequencies. The coherence of the charge transfer between the two donors is probed by Landau–Zener–St¨uckelberg interferometry. Single-charge transfer at zero bias (electron pumping) has been performed and the crossover between the adiabatic and non-adiabatic regimes is studied. Keywords: semiconductor physics, single dopants, nanoelectronics (Some figures may appear in colour only in the online journal)
in the compact structure of an advanced nanowire MOS-FET, where a maximum coupling with the electrodes is targeted. One way to increase the distance between the donor and the S-D while preserving a good device conductance is to use tunnel transport through a chain of donors [6]. Depending on the separation between the S-D electrodes and the density of donors, resonant tunneling through two donors in series can be much larger than resonant tunneling through one centered donor or than direct tunneling between S-D [6–8]. We call the coupled atom transistor (CAT) a transistor in which two shallow donors are tunnel coupled in series to S-D and their atomic levels controlled by gates. As we will see 3 independent gates are necessary to control the CAT. The first advantage of the CAT is that the spectroscopy of shallow donors is cleaner than in the SAT. Not only the larger distance between the S-D make them less invasive, but the discrete orbital of one donor serves as a sharp energy filter to perform the spectroscopy of the second donor. This spectroscopy allows to investigate the influence of the local environment on the valley-splitting (difference in energy between the ground and first excited states) for donors in silicon [9]. This splitting should remain large enough to manipulate coherently the donor’s orbitals. We measure 10 meV (≈100 K), a comfortable value for manipulating single
1. Introduction
Thanks to size shrinking, solid-state devices have entered a new era where single atoms can be electrically connected between a source and a drain (S-D) and their quantum levels controlled by capacitively coupled gate electrodes. Going down to a single atom, namely in this work substitutional donors (P or As) in a silicon crystal, we obtain the so-called single atom transistor (SAT) [1, 2]. The voltage applied to the electrodes adds to the attractive potential of the donor atom and controls the global confinement potential landscape seen by electrons. A drainsource current Ids appears in the resonant tunneling regime when the ground state of such a donor lies between the Fermi levels defined by the S-D under a voltage bias Vds . Despite its apparent simplicity, the electrostatic problem of a SAT turns to be very complex. First the S-D are not perfect reservoirs (or voltage sources): their fluctuating, local density-of-states blurs the donor’s spectroscopy and electrons located inside the barriers separating the donor from the source and drain (barriers can contain a residual level of doping) dramatically affect electrical transport [1, 3, 4]. Secondly the local environment, consisting of charges, electric fields and different interfaces (and their resulting image charges) modify the donor state’s properties [5]. These effects are enhanced 0953-8984/15/154206+08$33.00
1
© 2015 IOP Publishing Ltd Printed in the UK
J. Phys.: Condens. Matter 27 (2015) 154206
X Jehl et al
Figure 1. 3D sketch of the CAT structure. (a) Lateral view after gate etching. Crystalline silicon in light pink, SiO2 in brown, polysilicon gate in dark pink. Two top gates partially overlap the silicon-on-insulator (SOI) nanowire (NW) channel. The gap between the gates Sgg is 30–35 nm. A 145 nm thick buried oxide (BOX) separates the silicon substrate from the SOI, used as a backgate. (b) View after thick Si3 N4 spacers deposition and etching (yellow).
orbitals at T = 4.2 K. This means that the energy spectrum is dominated by the core confinement potential at the sub-nm range around the donor atom, even if the tail of the orbitals (extending beyond 10 nm) can be tuned by gates to connect to the S-D. The small inelastic component to Ids observed in our CAT is also very encouraging in the perspective of isolating orbitals from environment and decreasing dephasing. Moreover the CAT offers many new functionalities such as electron pumping, charge qubits or steep slope switches and is also the device with 3 gates and 2 donors proposed by Kane [10]. Other schemes using the electron spin [11] or the charge [12] use fairly similar designs. At the moment the demonstration of coupled qubits based on single donors (and even the control of exchange between them) has not been done. The demonstration of a CAT with doubly occupied donors states (D− ) is also to be done. The sensitivity of the exchange interaction to the qubit location as well as the shallow nature of the D− state are important issues [13]. The paper is organized as follows: we first describe our CAT fabrication scheme with shallow donors in the channel (channel doping or tilted S-D implantation) and the associated process simulation (section 2). Then we show how to choose the control voltages to obtain the different regimes of the corner states (when electrons are pushed in the corners of the nanowire, section 3.1) or the CAT (when electrons are repelled towards the body of the nanowire, section 3.2). The role of other charges in the environment is discussed in section 3.3. The results are presented in section 4, with donor spectroscopy (section 4.1), Landau–Zener–Stuckelberg interferometry (section 4.2) and electron pumping (section 4.3).
20 nm thick etched nanowire is partially covered by two, 40 nm long polycrystalline silicon top gates above a 5 nm thick front gate oxide (SiO2 ). these gates face each other at a distance of 30 nm (figure 1). 15 nm thick SiN spacers are formed around the gates. A major advantage of this structure is its compactness and the excellent control of the electric field by gates. It also allows co-integration with CMOS circuits, e.g. for reading or driving signals on-chip [44]. On the other hand the implanted donors see a complex environment, including heavily doped electrodes and dielectrics which can limit the coherence time. We use two methods to implant shallow donors in the channel: (i) The channel is doped with phosphorus at a concentration of 1024 m−3 before gate deposition. This method has been used in [15]. The heavily (Arsenic) doped S-D are separated by approximately 70 nm. The concentration is chosen to obtain a mean distance between donors of ≈10 nm, yielding a reasonable tunnel coupling (10– 100 µeV, depending on the cristal orientation [12, 16, 17]). The channel length is chosen so that resonant tunneling through 2 donors in series is more favorable than direct tunnel coupling between S-D (which becomes important at very short channel length) or resonant tunneling through 1 centered dopant (important at intermediate channel lengths like in the SAT of [18] where the gate length was 30 nm and source drain distance as small as 10– 20 nm). Typically the channel length is 3–4 times the mean distance between donors. This rough estimate is supported by simulations of the fabrication process shown in the next section. (ii) The channel is undoped (or Boron doped) and the highly doped drain (HDD) is performed with a large tilt angle (55◦ ). Depending on the tilt orientation (North-South (NS) or East-West (EW)), As donors are eventually implanted in the channel (EW case) or not (NS case), the channel being protected in the latter case (see figure 2). This is due to the masking effect of the gates and spacers.
2. Design and fabrication
We have designed CATs following an advanced CMOS nanowire transistor process flow [14], except for e-beam (instead of deep-UV) lithography to define the nanowire and two top gates with a separation down to 30 nm. Samples are fabricated on 200 or 300 mm Silicon-On-Insulator (SOI) wafers. For the CATs presented thereafter, the 60 nm wide and 2
J. Phys.: Condens. Matter 27 (2015) 154206
X Jehl et al
The device used in [15] is P-doped before a NS HDD implantation, while the one from [19] remained undoped before an EW As HDD implantation. The profile of the donors distribution is obtained by kinetic Monte-Carlo (KMC) simulations3 of the implantation/diffusion process. KMC simulations are 3D and include precisely the implantation and thermal budgets. They allow us to adjust the dose and sample layout to obtain the best geometry for CATs. Some results are shown in figure 2, comparing an NS (red, (a)–(c)) and an EW (blue, (d)–(g)) HDD implantation. During the tilted NS implantation the tall top gates protect the centre of the channel from implantation. In the case of EW, we observe that some As donors are implanted further towards the middle of the channel, in between the two gates. 3. Tunability and versatility of the CAT design
In our device the electric field is controlled by the 2 top gates and the S-D electrodes. Electric fields can be large (a few tens of meV nm−1 ) which is crucial for the control of the electronic orbitals by the Stark effect. Nevertheless a third gate is necessary to get the full control of the device (two gates for controlling the orbitals on the two donors and at least one gate for their coupling): for that purpose we bias the substrate which acts as a backgate [20]. The channel is separated from the substrate by a 145 nm buried oxide (BOX). With its 3 gates, the device is very versatile as the electrons can either be pushed in the upper corners of the nanowire or at its centre, towards the BOX. Figure 2. 2D top views of the kinetic Monte-Carlo (KMC) process simulation of the CAT structure at various tilted highly doped drain (HDD) implantations of As donors (blue). Red (green) spheres are phosphorus (or boron) dopants implanted during the channel doping step, before the formation of the gates. Nitride spacers are not represented. (a)–(c) North–south tilted implantation: the channel is protected against HDD As implantation by the top gates and spacers. (b) Without channel implantation: there is no donor in the channel between the gates. (c) With P channel implantation, donors are stochastically implanted in the channel; (d)–(g) east–west tilted implantation: (e)–(g) different tilt angle: (e) at small angle the channel is free from As donors thanks to masking by the spacers; (f ) and (g) at large angle the channel is only partially masked during HDD and a few As atoms form a quasi 1D path through the channel (with (f ) or without (g) Boron channel implantation).
3.1. Corner states at negative substrate voltage
At negative substrate bias Vbg and positive front gate voltages the electrons are pushed towards the upper corners of the nanowire. Figure 3 shows the S-D current as function of these voltages (with Vg1 = Vg2 ). At T = 0.15 K, above the red dashed line which defines this regime, clear Coulomb oscillations are seen due to the two quantum dots formed by accumulation of electrons in the corners [21]. This effect has been studied in [22]: both accumulation channels are connected to source and drain through the two tunnel barriers formed by the weakly doped silicon regions below the spacers [21]. Two quantum dots are then formed which are capacitively coupled. The current map in the Vg1 − Vg2 plane in this regime exhibits a typical honeycomb pattern: S-D current arises when the number of electrons in one of the dots changes by one unit (see figure 4(a), top right corner, at the onset of this regime for Vbg = +11.5 V).
shallow donors. Below the threshold for the accumulation channel the S-D current at low temperature is dominated by resonant transport through 2 phosphorus donors in series [15]. This occurs at low energy (negative top gate voltages), when the electronic orbitals around the donors are not hybridized with the corner states. Near the onset of the conduction band the electronic orbitals are more extended and a centered hybridized state [5] can be well connected to both source and drain such that a line of current appears in the 2D plot (for instance the line crossing around Vg1 = Vg2 = −0.55 V, also visible in figure 3 at Vbg = +11.5 V, see red arrow). Much below the onset of conduction, only current through two dopants connected in series can be observed, when their energy levels (each of them controlled preferentially by one
3.2. Donors at positive substrate voltage
At positive Vbg , electrons in the constriction are pushed near the BOX interface. When strong negative voltages are applied on both top gates, electrons are driven from the S-D through a constriction of nominal width W = 30 nm. The conduction channel has the shape of a tunable constriction squeezed by a split top gate. This constriction contains a few phosphorus 3
Synopsys SProcess KMC v.G-2012.06. 3
J. Phys.: Condens. Matter 27 (2015) 154206
X Jehl et al
taken into account at least in a mean field approach [28, 31]. The ionization of donors in the graded concentration extension regions of the S-D (and possibly of other offset charges) influences the transport spectroscopy through centered donors in the channel in various ways: they can produce lines of differential conductance at finite bias, mimicking the presence of excited states for the centered donors [1, 3], they can suppress the S-D tunnel current and they can reduce the charge dephasing time. 4. Results
We used our CAT to obtain 3 major results which illustrate the potentialities of this device.
Figure 3. Drain-source current versus Vbg and Vg1 =Vg2 (gate
voltages) at T = 0.15 K. Above the dashed red line Coulomb blockade oscillations are observed for the MOS-single electron transistors formed by accumulation in the upper corners of the nanowire. Below the dashed red line the current is due to resonant tunneling through single donors or hybridized surface-donor states. The line at the lowest energy (large negative Vg1 = Vg2 ) highlighted by the red arrow is through the same donor than the line crossing at Vg1 = Vg2 = −0.55 V on figure 4. Note the proliferation of lines at higher energy when the donors states are close to the onset of the conduction band.
4.1. Valley-orbit splitting for P donors
We performed the spectroscopy of an isolated phosphorus donor using the second donor as an efficient energy filter [15]. This consists in increasing Vds as in figure 4 up to the point where the first excited state of the donor enters in the energy window between the Fermi energies in the source and drain (see figure 6). Compared to the spectroscopy performed using a SAT, this method avoids completely the influence of the S-D electrodes and of the offset charges. We measured a large valley-orbit splitting of 10 ± 0.5 meV, in agreement with theoretical simulations for a P donor located 3 nm away from the Si/SiO2 interface. The calculation includes the actual geometry of the sample, the screening effects and the electric field. The large valley-orbit splitting is only slightly decreased compared to its value for a phosphorus atom in bulk silicon (13.7 meV) [9, 32, 33]. This means that the wave function for electrons near the core potential of the phosphorus atom is not dramatically affected by the mesoscopic environment of the trigate MOSFET [5, 34–37], an essential result to further build electronic functionalities based on shallow donors in silicon.
gate) are aligned (see figure 4). In the 2D plot of figure 4 at small Vds = 2 mV this condition only occurs at two triple points [15, 23]. 3.3. The role of other donors and charge states in the nearby environment
Figures 3 and 4 show that the identification of the ionization line to shallow donors becomes very complex as they start hybridizing with the conduction band states. This is because the bottom of the conduction band exhibits a band (‘Lifshitz’) tail in the presence of spatial disorder. In this tail (after averaging over disorder) the density-of-states is exponential in energy. Only at low energy it is small enough that a couple of donors can be identified and well separated in energy and space from other environmental states. Of course without the 3 control voltages it would have been impossible to find by chance the matching between the two shallow donor states. The limited number of donors in the channel allows to map the donors configuration in the channel thanks to tunnel spectroscopy, varying the substrate and the front gate voltages [24–28]. This technique could be applied to short enough samples where all the shallow donors are well connected to both S-D. Figure 5 shows the map of the S-D conductance versus the control gate voltages in a sample similar to the one used in [18]. For 3 donors (respectively called A–C) involved the map of ionization lines can be reliably indexed and the double occupation of each donor (resp. A –C , strictly parallel to respectively A–C) can be tracked [28]. The back gate also allows to modify the valley population of the donor as it gets hybridized with the conduction band states [29]. For a larger number of donors the map becomes very complex (simulation and experimental results not shown) [30]. Even with a few donors the electrostatic problem is complex also because the ionization of donors at the edge of the S-D contact should be
¨ 4.2. Landau–Zener–Stuckelberg interferometry
We performed a first step towards building more complex architectures based on series of single dopant elements connected together by demonstrating the first coherent charge transfer between 2 donors connected in series [19]. In this experiment we address the ground state of two dopants and use a microwave drive to coherently exchange a charge between the two dopants. Our system presents unique opportunities as the two donors implanted in the channel appear to be well isolated from the environnement. Indeed, as can be seen on figure 6 co-tuneling is negligible. It means that, with appropriate gate voltages, the current mostly flows through the two dopants connected in series. The second important aspect for the device is high frequency operation, with a speed that can potentially reach 1 THz. This fast operation is possible thanks to the large energy window available around the dopants ground states, without other states through which the current could leak: As demonstrated by the spectroscopic measurement (figure 6), the first excited state is located more than 10 meV above the ground state. 4
J. Phys.: Condens. Matter 27 (2015) 154206
X Jehl et al
Figure 4. (a) Source-Drain current (Ids ) in the CAT at T = 0.1 K, Vds = 2 mV and Vbg = 11.5 V. In the upper right corner two parallel quantum dots are accumulated below the 2 front gates (above the red dashed line on figure 3). A typical honeycomb pattern is observed. In the bottom left corner the channel is pushed in the central bottom part of the channel, which becomes a tunable constriction squeezed by a split top gate and containing a few phosphorus shallow donors. The red arrow indicates the same donor line than in figure 3. At even lower energy (gate voltage) transport is dominated by resonant transport through two P donor states coupled in series (red circle) [15]. (b) Ids at T = 0.1 K, Vbg = 11.5 V and Vds = 3 mV. At finite Vds the two triple points P1 and P2 (in red) turn into two triangles. The white dashed lines indicate the edges of these triangles for Vds = −3 mV. The trajectory Vg∗ used in figure 8 is the orange dashed axis joining the two triple points in red.
(a) -0.70
Ids (pA)
Vg2 (V)
5 -0.75
4 3
-0.80
2 1
-0.85
0
-0.64
-0.62
-0.60
-0.58
-0.56
Vg1 (V) 16 16 mV 18 mV 20 mV
Ids (pA)
12
Figure 5. (a) Source-drain differential conductance versus gate bias
at T = 4.2 K. The dashed line is the simulated threshold voltage of a device without donors. Six ionization lines noted A–C are observed to come by pairs. This is attributed to the As+, As0 and Asionization lines resulting from the double occupation of 3 different donors. States with more than 4 electrons are barely defined because of the strong coupling with the conduction band. According to our simulation the donor corresponding to lines (C, C ) is closer to the front gate than the two donors of the A–B ionization lines. Inset: schematics of the sample cross-section. See [22] for more details.
8 4 0
0
5
10 ε (meV)
15
20
Figure 6. (a) Ids in the CAT versus both gate voltages Vg1 and Vg2 at T = 0.15 K, Vbg = 11.5 V and Vds = 16 mV. The line parallel to the base is due to the alignment of the excited state of one donor with the ground state of the other donor. (b) Cuts through the triangles at various Vds (the cut is through the broken line in (a) for Vds = 16 mV). The distance in energy between the ground and first excited state gives a valley splitting of 10 ± 0.5 meV. See section 4.1 and [15] for more details.
To demonstrate coherent charge exchange between the two dopants, the gate voltages are tuned such that the dopants ground-state levels are arranged like depicted in figure 7(a), i.e. within a bias window Vds , but far away from the Fermi levels of the leads. A microwave signal is applied in order to sweep one level position with respect to the other. The corresponding time evolution of the levels under microwave drive is depicted in figure 7(b). At each anticrossing a
Landau–Zener tunneling process can occur. The tunneling amplitudes of successive anticrossings can interfere when the two-donor system preserves quantum coherence between successive anticrossings [38]. The current through the 5
J. Phys.: Condens. Matter 27 (2015) 154206
X Jehl et al
Figure 7. (a) Schematics of the Landau–Zener experiment, with the oscillating detuning 0 (t) between the energy levels. (b) Crossing of the energy levels. (c) Development of the interference pattern as the frequency increases. (d) Corresponding evolution of the driving frequency compared to the charge coherence time T2 . See section 4.2 and [19] for more details.
system then shows a characteristic Landau–Zener–St¨uckelberg interference pattern as shown in figure 7(c), where Ids is recorded as a function of the static level detuning 0 between the two donors and of the microwave amplitude VMW for a certain microwave drive frequency fMW and for Vds = 5 mV. The first striking feature is a set of equally spaced, horizontal current ridges located at 0 = ±nhfMW where h is the Planck constant and n an integer. These ridges reflect tunneling currents assisted by the emission (for 0 > 0) or the absorption (for 0 < 0) of n photons [39]. The second noticeable feature is a strong current modulation along each ridge, a quantum interference effect between two possible paths with or without Landau–Zener transition between successive anticrossings of electronic levels on the two donors. This effect is analogous to Mach–Zehnder interferometry for optical photons. The whole current map is fully described by theoretical models [19, 38] from which one can extract the coherence time T2 [19]. A rough estimate of this time is easily accessible by comparing the features of Landau–Zener–St¨uckelberg interference maps acquired for various drive frequencies (see figures 7(c) and (d)). When the drive frequency is large compared to the inverse of the charge coherence time T2 , the Landau–Zener–St¨uckelberg pattern is fully developped. When the drive frequency is progressively decreased, the interference structure is lost, up to the point where the interference pattern is completely blurred (see figure 7(d)). In agreement with this estimate, precise calculations from fits to the interference pattern [19] give a charge coherence time T2 = 0.3 ± 0.1 ns. The limitation to the coherence time could arise from the escape tunneling time to drain or from charge noise induced by the gates or switching offset charges (see section 3.3). This T2 value is comparable to other semiconductor charge qubits [40, 41], however, in our case the large frequency window available offers the possiblity to manipulate the charge states very quickly and perform several operations within the coherence time.
4.3. Electron pump based on two shallow donors
We realized the first electron pump based on two donors in series [42]. To achieve pumping through two atoms, we set Vds to zero and modulate the top gates with phase-shifted sinewaves added to the dc voltages, in order to follow elliptic trajectories in the (Vg1 − Vg2 ) plane possibly enclosing a triple point. When turning around the lower red point of figure 4(b), the following charge state (N1, N2) sequence is realized: (0, 0) → (1, 0) → (0, 1) → (0, 0), leading to the net transfer of one electron in one direction. For the upper red point, the sequence (1, 1) → (1, 0) → (0, 1) → (1, 1) leads to a current in the other direction. Each of the above cycles results in the transfer of one electron from source to drain at the driving frequency f . Adiabatic pumping occurs when f1 is much larger than the timescale associated with tunneling for an electron in the two-donor system. We achieved quantized pumping in the low frequency adiabatic regime and verify that the delivered current follows Ids = ef (see figure 8). The small deviation from this relation in the adiabatic regime are higher order tunneling events, for instance an electron tunneling through two barriers at the same time. The quest for high accuracy electron pumping is of major importance for metrology purposes, so these higher order tunneling events have to be controlled. The donor-based electron pump has inherent advantages as compared to other adiabatic electron pump because of its large Coulomb confinement which prevents from cotunneling. Yet a good control of the different tunnel rates is required to fabricate an electron pump with state-of-the-art precision. At higher frequency the pumped current deviates from Ids = ef . New regions of finite current appear in the current map, for elliptic trajectories which do not enclose a triple point. They occur when the charge transfer is limited by one of the tunneling rates. The multiple different regions available in the current map correspond to as many different pumping sequences that emphasizes a particular tunneling event. By 6
J. Phys.: Condens. Matter 27 (2015) 154206
X Jehl et al
Figure 8. (a) Pumped current through two donors in series at Vds = 0 V, when the trajectory resulting from the ac drives on the gates encloses a triple point. Vg∗ is the gate trajectory depicted in figure 4. (b) This current matches the relation Ids = ±ef (dashed lines), where f is the driving frequency. See section 4.3 and [42] for more details.
carefully analyzing the pumping current map, we are able to understand the electron dynamics in the two-donor system. We modeled the transitions between quantum states as Landau– Zener transitions and reproduced in detail the characteristic signatures observed in the non-adiabatic regime for any elliptic trajectories [42].
References [1] Pierre M, Hofheinz M, Jehl X, Sanquer M, Molas G, Vinet M and Deleonibus 2009 Eur. Phys. J. B 70 475 [2] Fuechsle M, Miwa J A, Mahapatra S, Ryu H, Lee S, Warschkow O, Hollenberg L C L, Klimeck G and Simmons M Y 2012 Nat. Nano. 7 242 [3] Hofheinz M, Jehl X, Sanquer M, Molas G, Vinet M and Deleonibus S 2006 Eur. Phys. J. B 54 299 [4] Golovach V N, Jehl X, Houzet M, Pierre M, Roche B, Sanquer M and Glazman L I 2011 Phys. Rev. B 83 075401 [5] Rahman R, Lansbergen G P, Park S H, Verduijn J, Klimeck G, Rogge S and Hollenberg L C L 2009 Phys. Rev. B 80 165314 [6] Webb R A, Hartstein A, Wainer J J and Fowler A B 1985 Phys. Rev. Lett. 54 1577 [7] Larkin A I and Matveev K A 1987 Sov. Phys.—JETP 66 580 [8] Matveev K A and Larkin A I 1992 Phys. Rev. B 46 15337 [9] Ramdas A K and Rodriguez S 1981 Rep. Prog. Phys. 44 1297 [10] Kane B E 1998 Nature 393 133 [11] Vrijen R, Yablonovitch E, Wang K, Jiang H W, Balandin A, Roychowdhury V, Mor T and DiVincenzo D 2000 Phys. Rev. A 62 012306 [12] Hollenberg L C L, Dzurak A S, Wellard C, Hamilton A R, Reilly D J, Milburn G J and Clark R G 2004 Phys. Rev. B 69 113301 [13] Hill C D, Hollenberg L C L, Fowler A G, Welleard C J, Greentree A D and Goan H-S 2005 Phys. Rev. B 72 045350 [14] Barraud S et al 2012 IEEE Electron Device Lett. 33 1526 [15] Roche B, Dupont-Ferrier E, Voisin B, Cobian M, Jehl X, Wacquez R, Vinet M, Niquet Y-M and Sanquer M 2012 Phys. Rev. Lett. 108 206812 [16] Miller A and Abrahams E 1960 Phys. Rev. 120 745 [17] Hu X, Koiller B and Das Sarma S 2005 Phys. Rev. B 71 235332 [18] Pierre M, Wacquez R, Jehl X, Sanquer M, Vinet M and Cueto O 2010 Nat. Nano. 5 133 [19] Dupont-Ferrier E, Roche B, Voisin B, Jehl X, Wacquez R, Vinet M, Sanquer M and De Franceschi S 2013 Phys. Rev. Lett. 110 136802 [20] Roche B, Voisin B, Jehl X, Wacquez R, Sanquer M, Vinet M, Deshpande V and Previtali B 2012 Appl. Phys. Lett. 100 032107
5. Conclusions
We presented the first realization of a coupled atom transistor. We used a CMOS Silicon-on-Insulator nanowire process with special split gates designs and donor implantation. One big advantage of this structure is its compactness and the excellent control of the electric field by gates in a very small volume. The compacity makes the qubit integration and scaling easier but also reduces the volume for parasitic fluctuators. Of course the complex local environment seen by the two implanted donors should be treated carefully. We showed that the large quantization of orbitals for electrons trapped on shallow donors is preserved even in the presence of surrounding dielectric interfaces. The measured charge coherence time in our CAT is similar to what has been measured in other charge qubits and much larger than the estimated operating time. The next steps are the measurement of exchange between two shallow donors and the fabrication of a coupled charge-or-spin qubit based on single donors. The exchange has been measured recently for two coupled clusters of ≈2, 3 P donors [43]. The demonstration of a CAT with doubly occupied donors states (D− ) also remains to be done. On the design side, sample layouts with more gates and devices will be fabricated and investigated in order to benefit from single-dopant electronics co-integrated with classical CMOS circuits. Acknowledgments
The authors acknowledge financial support from the EU under Projects TOLOP, SiAM, AFSiD and the ERC Starting Grant HybridNano. 7
J. Phys.: Condens. Matter 27 (2015) 154206
X Jehl et al
[21] Hofheinz M, Jehl X, Sanquer M, Molas G, Vinet M and Deleonibus S 2006 Appl. Phys. Lett. 89 143504 [22] Voisin B et al 2014 Nano Lett. 14 2094 [23] van der Wiel W G, De Franceschi S, Elzerman J M, Fujisawa T, Tarucha S and Kouwenhoven L P 2003 Rev. Mod. Phys. 75 1 [24] Ono Y, Morizur J-F, Nishiguchi K, Takashina K, Yamaguchi H, Hiratsuka K, Horiguchi S, Inokawa H and Takahashi Y 2006 Phys. Rev. B 74 235317 [25] Khalafalla M A H, Ono Y, Nishiguchi K and Fujiwara A 2007 Appl. Phys. Lett. 91 263513 [26] Khalafalla M A H, Ono Y, Nishiguchi K and Fujiwara A 2009 Appl. Phys. Lett. 94 223501 [27] Mohiyaddin F A, Rahman R, Kalra R, Klimeck G, Hollenberg L C L, Pla J J, Dzurak A S and Morello A 2013 Nano Lett. 13 1903 [28] Voisin B, Cobian M, Jehl X, Vinet M, Niquet Y-M, Delereue C, de Franceschi S and Sanquer M 2014 Phys. Rev. B 89 161404 [29] Verduijn J, Tettamanzi G C and Rogge S 2013 Nano Lett. 13 1476 [30] Efros A L and Shklovskii B I 1975 J. Phys. C: Solid State Phys. 8 L49 [31] Oh J H, Ahn D, Yu Y S and Hwang S W 2008 Phys. Rev. B 77 035313
[32] Kohn W and Luttinger J M 1955 Phys. Rev. 98 915 [33] Aggarwal R L and Ramdas A K 1965 Phys. Rev. 140 A1246 [34] Diarra M, Niquet Y-M, Delerue C and Allan G 2007 Phys. Rev. B 75 045301 [35] Hao Y L, Djotyan A P, Avetisyan A A and Peeters F M 2009 Phys. Rev. B 80 035329 [36] Calderon M J, Verduijn J, Lansbergen G P, Tettamanzi G C, Rogge S and Koiller B 2010 Phys. Rev. B 82 075317 [37] Saraiva A L, Koiller B and Friesen M 2010 Phys. Rev. B 82 245314 [38] Shevchenko S, Ashhab S and Nori F 2010 Phys. Rep. 492 1 [39] Stoof T H and Nazarov Y V 1996 Phys. Rev. B 53 1050 [40] Hayashi T, Fujisawa T, Cheong H D, Jeong Y H and Hirayama Y 2003 Phys. Rev. Lett. 91 226804 [41] Petta J R, Johnson A C, Marcus C M, Hanson M P and Gossard A C 2004 Phys. Rev. Lett. 93 186802 [42] Roche B, Riwar R-P, Voisin B, Dupont-Ferrier E, Wacquez R, Vinet M, Sanquer M, Splettstoesser J and Jehl X 2013 Nat. Commun. 4 1581 [43] Weber B, Tan Y H M, Mahapatra S, Watson T F, Ryu H, Rahman R, Hollenberg L C L, Klimeck G and Simmons M Y 2014 Nat. Nano. 9 430 [44] Clapera P et al unpublished
8
Search
Collections
Journals
About
Contact us
My IOPscience
The coupled atom transistor
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 J. Phys.: Condens. Matter 27 154206 (http://iopscience.iop.org/0953-8984/27/15/154206) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 169.230.243.252 This content was downloaded on 24/03/2015 at 07:34
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 154206 (8pp)
doi:10.1088/0953-8984/27/15/154206
The coupled atom transistor X Jehl1 , B Voisin1 , B Roche1 , E Dupont-Ferrier1 , S De Franceschi1 , 2 ´ , O Cueto2 , M Sanquer1 , M Cobian1 , Y-M Niquet1 , B Sklenard 2 2 R Wacquez and M Vinet 1 University Grenoble Alpes, INAC, F-38000 Grenoble, France and CEA, INAC-SPSMS, F-38054 Grenoble, France 2 University Grenoble Alpes, LETI, F-38000 Grenoble, France and CEA, LETI, Minatec campus, F-38054 Grenoble, France
E-mail: [email protected] Received 30 July 2014, revised 20 January 2015 Accepted for publication 22 January 2015 Published 18 March 2015 Abstract
We describe the first implementation of a coupled atom transistor where two shallow donors (P or As) are implanted in a nanoscale silicon nanowire and their electronic levels are controlled with three gate voltages. Transport spectroscopy through these donors placed in series is performed both at zero and microwave frequencies. The coherence of the charge transfer between the two donors is probed by Landau–Zener–St¨uckelberg interferometry. Single-charge transfer at zero bias (electron pumping) has been performed and the crossover between the adiabatic and non-adiabatic regimes is studied. Keywords: semiconductor physics, single dopants, nanoelectronics (Some figures may appear in colour only in the online journal)
in the compact structure of an advanced nanowire MOS-FET, where a maximum coupling with the electrodes is targeted. One way to increase the distance between the donor and the S-D while preserving a good device conductance is to use tunnel transport through a chain of donors [6]. Depending on the separation between the S-D electrodes and the density of donors, resonant tunneling through two donors in series can be much larger than resonant tunneling through one centered donor or than direct tunneling between S-D [6–8]. We call the coupled atom transistor (CAT) a transistor in which two shallow donors are tunnel coupled in series to S-D and their atomic levels controlled by gates. As we will see 3 independent gates are necessary to control the CAT. The first advantage of the CAT is that the spectroscopy of shallow donors is cleaner than in the SAT. Not only the larger distance between the S-D make them less invasive, but the discrete orbital of one donor serves as a sharp energy filter to perform the spectroscopy of the second donor. This spectroscopy allows to investigate the influence of the local environment on the valley-splitting (difference in energy between the ground and first excited states) for donors in silicon [9]. This splitting should remain large enough to manipulate coherently the donor’s orbitals. We measure 10 meV (≈100 K), a comfortable value for manipulating single
1. Introduction
Thanks to size shrinking, solid-state devices have entered a new era where single atoms can be electrically connected between a source and a drain (S-D) and their quantum levels controlled by capacitively coupled gate electrodes. Going down to a single atom, namely in this work substitutional donors (P or As) in a silicon crystal, we obtain the so-called single atom transistor (SAT) [1, 2]. The voltage applied to the electrodes adds to the attractive potential of the donor atom and controls the global confinement potential landscape seen by electrons. A drainsource current Ids appears in the resonant tunneling regime when the ground state of such a donor lies between the Fermi levels defined by the S-D under a voltage bias Vds . Despite its apparent simplicity, the electrostatic problem of a SAT turns to be very complex. First the S-D are not perfect reservoirs (or voltage sources): their fluctuating, local density-of-states blurs the donor’s spectroscopy and electrons located inside the barriers separating the donor from the source and drain (barriers can contain a residual level of doping) dramatically affect electrical transport [1, 3, 4]. Secondly the local environment, consisting of charges, electric fields and different interfaces (and their resulting image charges) modify the donor state’s properties [5]. These effects are enhanced 0953-8984/15/154206+08$33.00
1
© 2015 IOP Publishing Ltd Printed in the UK
J. Phys.: Condens. Matter 27 (2015) 154206
X Jehl et al
Figure 1. 3D sketch of the CAT structure. (a) Lateral view after gate etching. Crystalline silicon in light pink, SiO2 in brown, polysilicon gate in dark pink. Two top gates partially overlap the silicon-on-insulator (SOI) nanowire (NW) channel. The gap between the gates Sgg is 30–35 nm. A 145 nm thick buried oxide (BOX) separates the silicon substrate from the SOI, used as a backgate. (b) View after thick Si3 N4 spacers deposition and etching (yellow).
orbitals at T = 4.2 K. This means that the energy spectrum is dominated by the core confinement potential at the sub-nm range around the donor atom, even if the tail of the orbitals (extending beyond 10 nm) can be tuned by gates to connect to the S-D. The small inelastic component to Ids observed in our CAT is also very encouraging in the perspective of isolating orbitals from environment and decreasing dephasing. Moreover the CAT offers many new functionalities such as electron pumping, charge qubits or steep slope switches and is also the device with 3 gates and 2 donors proposed by Kane [10]. Other schemes using the electron spin [11] or the charge [12] use fairly similar designs. At the moment the demonstration of coupled qubits based on single donors (and even the control of exchange between them) has not been done. The demonstration of a CAT with doubly occupied donors states (D− ) is also to be done. The sensitivity of the exchange interaction to the qubit location as well as the shallow nature of the D− state are important issues [13]. The paper is organized as follows: we first describe our CAT fabrication scheme with shallow donors in the channel (channel doping or tilted S-D implantation) and the associated process simulation (section 2). Then we show how to choose the control voltages to obtain the different regimes of the corner states (when electrons are pushed in the corners of the nanowire, section 3.1) or the CAT (when electrons are repelled towards the body of the nanowire, section 3.2). The role of other charges in the environment is discussed in section 3.3. The results are presented in section 4, with donor spectroscopy (section 4.1), Landau–Zener–Stuckelberg interferometry (section 4.2) and electron pumping (section 4.3).
20 nm thick etched nanowire is partially covered by two, 40 nm long polycrystalline silicon top gates above a 5 nm thick front gate oxide (SiO2 ). these gates face each other at a distance of 30 nm (figure 1). 15 nm thick SiN spacers are formed around the gates. A major advantage of this structure is its compactness and the excellent control of the electric field by gates. It also allows co-integration with CMOS circuits, e.g. for reading or driving signals on-chip [44]. On the other hand the implanted donors see a complex environment, including heavily doped electrodes and dielectrics which can limit the coherence time. We use two methods to implant shallow donors in the channel: (i) The channel is doped with phosphorus at a concentration of 1024 m−3 before gate deposition. This method has been used in [15]. The heavily (Arsenic) doped S-D are separated by approximately 70 nm. The concentration is chosen to obtain a mean distance between donors of ≈10 nm, yielding a reasonable tunnel coupling (10– 100 µeV, depending on the cristal orientation [12, 16, 17]). The channel length is chosen so that resonant tunneling through 2 donors in series is more favorable than direct tunnel coupling between S-D (which becomes important at very short channel length) or resonant tunneling through 1 centered dopant (important at intermediate channel lengths like in the SAT of [18] where the gate length was 30 nm and source drain distance as small as 10– 20 nm). Typically the channel length is 3–4 times the mean distance between donors. This rough estimate is supported by simulations of the fabrication process shown in the next section. (ii) The channel is undoped (or Boron doped) and the highly doped drain (HDD) is performed with a large tilt angle (55◦ ). Depending on the tilt orientation (North-South (NS) or East-West (EW)), As donors are eventually implanted in the channel (EW case) or not (NS case), the channel being protected in the latter case (see figure 2). This is due to the masking effect of the gates and spacers.
2. Design and fabrication
We have designed CATs following an advanced CMOS nanowire transistor process flow [14], except for e-beam (instead of deep-UV) lithography to define the nanowire and two top gates with a separation down to 30 nm. Samples are fabricated on 200 or 300 mm Silicon-On-Insulator (SOI) wafers. For the CATs presented thereafter, the 60 nm wide and 2
J. Phys.: Condens. Matter 27 (2015) 154206
X Jehl et al
The device used in [15] is P-doped before a NS HDD implantation, while the one from [19] remained undoped before an EW As HDD implantation. The profile of the donors distribution is obtained by kinetic Monte-Carlo (KMC) simulations3 of the implantation/diffusion process. KMC simulations are 3D and include precisely the implantation and thermal budgets. They allow us to adjust the dose and sample layout to obtain the best geometry for CATs. Some results are shown in figure 2, comparing an NS (red, (a)–(c)) and an EW (blue, (d)–(g)) HDD implantation. During the tilted NS implantation the tall top gates protect the centre of the channel from implantation. In the case of EW, we observe that some As donors are implanted further towards the middle of the channel, in between the two gates. 3. Tunability and versatility of the CAT design
In our device the electric field is controlled by the 2 top gates and the S-D electrodes. Electric fields can be large (a few tens of meV nm−1 ) which is crucial for the control of the electronic orbitals by the Stark effect. Nevertheless a third gate is necessary to get the full control of the device (two gates for controlling the orbitals on the two donors and at least one gate for their coupling): for that purpose we bias the substrate which acts as a backgate [20]. The channel is separated from the substrate by a 145 nm buried oxide (BOX). With its 3 gates, the device is very versatile as the electrons can either be pushed in the upper corners of the nanowire or at its centre, towards the BOX. Figure 2. 2D top views of the kinetic Monte-Carlo (KMC) process simulation of the CAT structure at various tilted highly doped drain (HDD) implantations of As donors (blue). Red (green) spheres are phosphorus (or boron) dopants implanted during the channel doping step, before the formation of the gates. Nitride spacers are not represented. (a)–(c) North–south tilted implantation: the channel is protected against HDD As implantation by the top gates and spacers. (b) Without channel implantation: there is no donor in the channel between the gates. (c) With P channel implantation, donors are stochastically implanted in the channel; (d)–(g) east–west tilted implantation: (e)–(g) different tilt angle: (e) at small angle the channel is free from As donors thanks to masking by the spacers; (f ) and (g) at large angle the channel is only partially masked during HDD and a few As atoms form a quasi 1D path through the channel (with (f ) or without (g) Boron channel implantation).
3.1. Corner states at negative substrate voltage
At negative substrate bias Vbg and positive front gate voltages the electrons are pushed towards the upper corners of the nanowire. Figure 3 shows the S-D current as function of these voltages (with Vg1 = Vg2 ). At T = 0.15 K, above the red dashed line which defines this regime, clear Coulomb oscillations are seen due to the two quantum dots formed by accumulation of electrons in the corners [21]. This effect has been studied in [22]: both accumulation channels are connected to source and drain through the two tunnel barriers formed by the weakly doped silicon regions below the spacers [21]. Two quantum dots are then formed which are capacitively coupled. The current map in the Vg1 − Vg2 plane in this regime exhibits a typical honeycomb pattern: S-D current arises when the number of electrons in one of the dots changes by one unit (see figure 4(a), top right corner, at the onset of this regime for Vbg = +11.5 V).
shallow donors. Below the threshold for the accumulation channel the S-D current at low temperature is dominated by resonant transport through 2 phosphorus donors in series [15]. This occurs at low energy (negative top gate voltages), when the electronic orbitals around the donors are not hybridized with the corner states. Near the onset of the conduction band the electronic orbitals are more extended and a centered hybridized state [5] can be well connected to both source and drain such that a line of current appears in the 2D plot (for instance the line crossing around Vg1 = Vg2 = −0.55 V, also visible in figure 3 at Vbg = +11.5 V, see red arrow). Much below the onset of conduction, only current through two dopants connected in series can be observed, when their energy levels (each of them controlled preferentially by one
3.2. Donors at positive substrate voltage
At positive Vbg , electrons in the constriction are pushed near the BOX interface. When strong negative voltages are applied on both top gates, electrons are driven from the S-D through a constriction of nominal width W = 30 nm. The conduction channel has the shape of a tunable constriction squeezed by a split top gate. This constriction contains a few phosphorus 3
Synopsys SProcess KMC v.G-2012.06. 3
J. Phys.: Condens. Matter 27 (2015) 154206
X Jehl et al
taken into account at least in a mean field approach [28, 31]. The ionization of donors in the graded concentration extension regions of the S-D (and possibly of other offset charges) influences the transport spectroscopy through centered donors in the channel in various ways: they can produce lines of differential conductance at finite bias, mimicking the presence of excited states for the centered donors [1, 3], they can suppress the S-D tunnel current and they can reduce the charge dephasing time. 4. Results
We used our CAT to obtain 3 major results which illustrate the potentialities of this device.
Figure 3. Drain-source current versus Vbg and Vg1 =Vg2 (gate
voltages) at T = 0.15 K. Above the dashed red line Coulomb blockade oscillations are observed for the MOS-single electron transistors formed by accumulation in the upper corners of the nanowire. Below the dashed red line the current is due to resonant tunneling through single donors or hybridized surface-donor states. The line at the lowest energy (large negative Vg1 = Vg2 ) highlighted by the red arrow is through the same donor than the line crossing at Vg1 = Vg2 = −0.55 V on figure 4. Note the proliferation of lines at higher energy when the donors states are close to the onset of the conduction band.
4.1. Valley-orbit splitting for P donors
We performed the spectroscopy of an isolated phosphorus donor using the second donor as an efficient energy filter [15]. This consists in increasing Vds as in figure 4 up to the point where the first excited state of the donor enters in the energy window between the Fermi energies in the source and drain (see figure 6). Compared to the spectroscopy performed using a SAT, this method avoids completely the influence of the S-D electrodes and of the offset charges. We measured a large valley-orbit splitting of 10 ± 0.5 meV, in agreement with theoretical simulations for a P donor located 3 nm away from the Si/SiO2 interface. The calculation includes the actual geometry of the sample, the screening effects and the electric field. The large valley-orbit splitting is only slightly decreased compared to its value for a phosphorus atom in bulk silicon (13.7 meV) [9, 32, 33]. This means that the wave function for electrons near the core potential of the phosphorus atom is not dramatically affected by the mesoscopic environment of the trigate MOSFET [5, 34–37], an essential result to further build electronic functionalities based on shallow donors in silicon.
gate) are aligned (see figure 4). In the 2D plot of figure 4 at small Vds = 2 mV this condition only occurs at two triple points [15, 23]. 3.3. The role of other donors and charge states in the nearby environment
Figures 3 and 4 show that the identification of the ionization line to shallow donors becomes very complex as they start hybridizing with the conduction band states. This is because the bottom of the conduction band exhibits a band (‘Lifshitz’) tail in the presence of spatial disorder. In this tail (after averaging over disorder) the density-of-states is exponential in energy. Only at low energy it is small enough that a couple of donors can be identified and well separated in energy and space from other environmental states. Of course without the 3 control voltages it would have been impossible to find by chance the matching between the two shallow donor states. The limited number of donors in the channel allows to map the donors configuration in the channel thanks to tunnel spectroscopy, varying the substrate and the front gate voltages [24–28]. This technique could be applied to short enough samples where all the shallow donors are well connected to both S-D. Figure 5 shows the map of the S-D conductance versus the control gate voltages in a sample similar to the one used in [18]. For 3 donors (respectively called A–C) involved the map of ionization lines can be reliably indexed and the double occupation of each donor (resp. A –C , strictly parallel to respectively A–C) can be tracked [28]. The back gate also allows to modify the valley population of the donor as it gets hybridized with the conduction band states [29]. For a larger number of donors the map becomes very complex (simulation and experimental results not shown) [30]. Even with a few donors the electrostatic problem is complex also because the ionization of donors at the edge of the S-D contact should be
¨ 4.2. Landau–Zener–Stuckelberg interferometry
We performed a first step towards building more complex architectures based on series of single dopant elements connected together by demonstrating the first coherent charge transfer between 2 donors connected in series [19]. In this experiment we address the ground state of two dopants and use a microwave drive to coherently exchange a charge between the two dopants. Our system presents unique opportunities as the two donors implanted in the channel appear to be well isolated from the environnement. Indeed, as can be seen on figure 6 co-tuneling is negligible. It means that, with appropriate gate voltages, the current mostly flows through the two dopants connected in series. The second important aspect for the device is high frequency operation, with a speed that can potentially reach 1 THz. This fast operation is possible thanks to the large energy window available around the dopants ground states, without other states through which the current could leak: As demonstrated by the spectroscopic measurement (figure 6), the first excited state is located more than 10 meV above the ground state. 4
J. Phys.: Condens. Matter 27 (2015) 154206
X Jehl et al
Figure 4. (a) Source-Drain current (Ids ) in the CAT at T = 0.1 K, Vds = 2 mV and Vbg = 11.5 V. In the upper right corner two parallel quantum dots are accumulated below the 2 front gates (above the red dashed line on figure 3). A typical honeycomb pattern is observed. In the bottom left corner the channel is pushed in the central bottom part of the channel, which becomes a tunable constriction squeezed by a split top gate and containing a few phosphorus shallow donors. The red arrow indicates the same donor line than in figure 3. At even lower energy (gate voltage) transport is dominated by resonant transport through two P donor states coupled in series (red circle) [15]. (b) Ids at T = 0.1 K, Vbg = 11.5 V and Vds = 3 mV. At finite Vds the two triple points P1 and P2 (in red) turn into two triangles. The white dashed lines indicate the edges of these triangles for Vds = −3 mV. The trajectory Vg∗ used in figure 8 is the orange dashed axis joining the two triple points in red.
(a) -0.70
Ids (pA)
Vg2 (V)
5 -0.75
4 3
-0.80
2 1
-0.85
0
-0.64
-0.62
-0.60
-0.58
-0.56
Vg1 (V) 16 16 mV 18 mV 20 mV
Ids (pA)
12
Figure 5. (a) Source-drain differential conductance versus gate bias
at T = 4.2 K. The dashed line is the simulated threshold voltage of a device without donors. Six ionization lines noted A–C are observed to come by pairs. This is attributed to the As+, As0 and Asionization lines resulting from the double occupation of 3 different donors. States with more than 4 electrons are barely defined because of the strong coupling with the conduction band. According to our simulation the donor corresponding to lines (C, C ) is closer to the front gate than the two donors of the A–B ionization lines. Inset: schematics of the sample cross-section. See [22] for more details.
8 4 0
0
5
10 ε (meV)
15
20
Figure 6. (a) Ids in the CAT versus both gate voltages Vg1 and Vg2 at T = 0.15 K, Vbg = 11.5 V and Vds = 16 mV. The line parallel to the base is due to the alignment of the excited state of one donor with the ground state of the other donor. (b) Cuts through the triangles at various Vds (the cut is through the broken line in (a) for Vds = 16 mV). The distance in energy between the ground and first excited state gives a valley splitting of 10 ± 0.5 meV. See section 4.1 and [15] for more details.
To demonstrate coherent charge exchange between the two dopants, the gate voltages are tuned such that the dopants ground-state levels are arranged like depicted in figure 7(a), i.e. within a bias window Vds , but far away from the Fermi levels of the leads. A microwave signal is applied in order to sweep one level position with respect to the other. The corresponding time evolution of the levels under microwave drive is depicted in figure 7(b). At each anticrossing a
Landau–Zener tunneling process can occur. The tunneling amplitudes of successive anticrossings can interfere when the two-donor system preserves quantum coherence between successive anticrossings [38]. The current through the 5
J. Phys.: Condens. Matter 27 (2015) 154206
X Jehl et al
Figure 7. (a) Schematics of the Landau–Zener experiment, with the oscillating detuning 0 (t) between the energy levels. (b) Crossing of the energy levels. (c) Development of the interference pattern as the frequency increases. (d) Corresponding evolution of the driving frequency compared to the charge coherence time T2 . See section 4.2 and [19] for more details.
system then shows a characteristic Landau–Zener–St¨uckelberg interference pattern as shown in figure 7(c), where Ids is recorded as a function of the static level detuning 0 between the two donors and of the microwave amplitude VMW for a certain microwave drive frequency fMW and for Vds = 5 mV. The first striking feature is a set of equally spaced, horizontal current ridges located at 0 = ±nhfMW where h is the Planck constant and n an integer. These ridges reflect tunneling currents assisted by the emission (for 0 > 0) or the absorption (for 0 < 0) of n photons [39]. The second noticeable feature is a strong current modulation along each ridge, a quantum interference effect between two possible paths with or without Landau–Zener transition between successive anticrossings of electronic levels on the two donors. This effect is analogous to Mach–Zehnder interferometry for optical photons. The whole current map is fully described by theoretical models [19, 38] from which one can extract the coherence time T2 [19]. A rough estimate of this time is easily accessible by comparing the features of Landau–Zener–St¨uckelberg interference maps acquired for various drive frequencies (see figures 7(c) and (d)). When the drive frequency is large compared to the inverse of the charge coherence time T2 , the Landau–Zener–St¨uckelberg pattern is fully developped. When the drive frequency is progressively decreased, the interference structure is lost, up to the point where the interference pattern is completely blurred (see figure 7(d)). In agreement with this estimate, precise calculations from fits to the interference pattern [19] give a charge coherence time T2 = 0.3 ± 0.1 ns. The limitation to the coherence time could arise from the escape tunneling time to drain or from charge noise induced by the gates or switching offset charges (see section 3.3). This T2 value is comparable to other semiconductor charge qubits [40, 41], however, in our case the large frequency window available offers the possiblity to manipulate the charge states very quickly and perform several operations within the coherence time.
4.3. Electron pump based on two shallow donors
We realized the first electron pump based on two donors in series [42]. To achieve pumping through two atoms, we set Vds to zero and modulate the top gates with phase-shifted sinewaves added to the dc voltages, in order to follow elliptic trajectories in the (Vg1 − Vg2 ) plane possibly enclosing a triple point. When turning around the lower red point of figure 4(b), the following charge state (N1, N2) sequence is realized: (0, 0) → (1, 0) → (0, 1) → (0, 0), leading to the net transfer of one electron in one direction. For the upper red point, the sequence (1, 1) → (1, 0) → (0, 1) → (1, 1) leads to a current in the other direction. Each of the above cycles results in the transfer of one electron from source to drain at the driving frequency f . Adiabatic pumping occurs when f1 is much larger than the timescale associated with tunneling for an electron in the two-donor system. We achieved quantized pumping in the low frequency adiabatic regime and verify that the delivered current follows Ids = ef (see figure 8). The small deviation from this relation in the adiabatic regime are higher order tunneling events, for instance an electron tunneling through two barriers at the same time. The quest for high accuracy electron pumping is of major importance for metrology purposes, so these higher order tunneling events have to be controlled. The donor-based electron pump has inherent advantages as compared to other adiabatic electron pump because of its large Coulomb confinement which prevents from cotunneling. Yet a good control of the different tunnel rates is required to fabricate an electron pump with state-of-the-art precision. At higher frequency the pumped current deviates from Ids = ef . New regions of finite current appear in the current map, for elliptic trajectories which do not enclose a triple point. They occur when the charge transfer is limited by one of the tunneling rates. The multiple different regions available in the current map correspond to as many different pumping sequences that emphasizes a particular tunneling event. By 6
J. Phys.: Condens. Matter 27 (2015) 154206
X Jehl et al
Figure 8. (a) Pumped current through two donors in series at Vds = 0 V, when the trajectory resulting from the ac drives on the gates encloses a triple point. Vg∗ is the gate trajectory depicted in figure 4. (b) This current matches the relation Ids = ±ef (dashed lines), where f is the driving frequency. See section 4.3 and [42] for more details.
carefully analyzing the pumping current map, we are able to understand the electron dynamics in the two-donor system. We modeled the transitions between quantum states as Landau– Zener transitions and reproduced in detail the characteristic signatures observed in the non-adiabatic regime for any elliptic trajectories [42].
References [1] Pierre M, Hofheinz M, Jehl X, Sanquer M, Molas G, Vinet M and Deleonibus 2009 Eur. Phys. J. B 70 475 [2] Fuechsle M, Miwa J A, Mahapatra S, Ryu H, Lee S, Warschkow O, Hollenberg L C L, Klimeck G and Simmons M Y 2012 Nat. Nano. 7 242 [3] Hofheinz M, Jehl X, Sanquer M, Molas G, Vinet M and Deleonibus S 2006 Eur. Phys. J. B 54 299 [4] Golovach V N, Jehl X, Houzet M, Pierre M, Roche B, Sanquer M and Glazman L I 2011 Phys. Rev. B 83 075401 [5] Rahman R, Lansbergen G P, Park S H, Verduijn J, Klimeck G, Rogge S and Hollenberg L C L 2009 Phys. Rev. B 80 165314 [6] Webb R A, Hartstein A, Wainer J J and Fowler A B 1985 Phys. Rev. Lett. 54 1577 [7] Larkin A I and Matveev K A 1987 Sov. Phys.—JETP 66 580 [8] Matveev K A and Larkin A I 1992 Phys. Rev. B 46 15337 [9] Ramdas A K and Rodriguez S 1981 Rep. Prog. Phys. 44 1297 [10] Kane B E 1998 Nature 393 133 [11] Vrijen R, Yablonovitch E, Wang K, Jiang H W, Balandin A, Roychowdhury V, Mor T and DiVincenzo D 2000 Phys. Rev. A 62 012306 [12] Hollenberg L C L, Dzurak A S, Wellard C, Hamilton A R, Reilly D J, Milburn G J and Clark R G 2004 Phys. Rev. B 69 113301 [13] Hill C D, Hollenberg L C L, Fowler A G, Welleard C J, Greentree A D and Goan H-S 2005 Phys. Rev. B 72 045350 [14] Barraud S et al 2012 IEEE Electron Device Lett. 33 1526 [15] Roche B, Dupont-Ferrier E, Voisin B, Cobian M, Jehl X, Wacquez R, Vinet M, Niquet Y-M and Sanquer M 2012 Phys. Rev. Lett. 108 206812 [16] Miller A and Abrahams E 1960 Phys. Rev. 120 745 [17] Hu X, Koiller B and Das Sarma S 2005 Phys. Rev. B 71 235332 [18] Pierre M, Wacquez R, Jehl X, Sanquer M, Vinet M and Cueto O 2010 Nat. Nano. 5 133 [19] Dupont-Ferrier E, Roche B, Voisin B, Jehl X, Wacquez R, Vinet M, Sanquer M and De Franceschi S 2013 Phys. Rev. Lett. 110 136802 [20] Roche B, Voisin B, Jehl X, Wacquez R, Sanquer M, Vinet M, Deshpande V and Previtali B 2012 Appl. Phys. Lett. 100 032107
5. Conclusions
We presented the first realization of a coupled atom transistor. We used a CMOS Silicon-on-Insulator nanowire process with special split gates designs and donor implantation. One big advantage of this structure is its compactness and the excellent control of the electric field by gates in a very small volume. The compacity makes the qubit integration and scaling easier but also reduces the volume for parasitic fluctuators. Of course the complex local environment seen by the two implanted donors should be treated carefully. We showed that the large quantization of orbitals for electrons trapped on shallow donors is preserved even in the presence of surrounding dielectric interfaces. The measured charge coherence time in our CAT is similar to what has been measured in other charge qubits and much larger than the estimated operating time. The next steps are the measurement of exchange between two shallow donors and the fabrication of a coupled charge-or-spin qubit based on single donors. The exchange has been measured recently for two coupled clusters of ≈2, 3 P donors [43]. The demonstration of a CAT with doubly occupied donors states (D− ) also remains to be done. On the design side, sample layouts with more gates and devices will be fabricated and investigated in order to benefit from single-dopant electronics co-integrated with classical CMOS circuits. Acknowledgments
The authors acknowledge financial support from the EU under Projects TOLOP, SiAM, AFSiD and the ERC Starting Grant HybridNano. 7
J. Phys.: Condens. Matter 27 (2015) 154206
X Jehl et al
[21] Hofheinz M, Jehl X, Sanquer M, Molas G, Vinet M and Deleonibus S 2006 Appl. Phys. Lett. 89 143504 [22] Voisin B et al 2014 Nano Lett. 14 2094 [23] van der Wiel W G, De Franceschi S, Elzerman J M, Fujisawa T, Tarucha S and Kouwenhoven L P 2003 Rev. Mod. Phys. 75 1 [24] Ono Y, Morizur J-F, Nishiguchi K, Takashina K, Yamaguchi H, Hiratsuka K, Horiguchi S, Inokawa H and Takahashi Y 2006 Phys. Rev. B 74 235317 [25] Khalafalla M A H, Ono Y, Nishiguchi K and Fujiwara A 2007 Appl. Phys. Lett. 91 263513 [26] Khalafalla M A H, Ono Y, Nishiguchi K and Fujiwara A 2009 Appl. Phys. Lett. 94 223501 [27] Mohiyaddin F A, Rahman R, Kalra R, Klimeck G, Hollenberg L C L, Pla J J, Dzurak A S and Morello A 2013 Nano Lett. 13 1903 [28] Voisin B, Cobian M, Jehl X, Vinet M, Niquet Y-M, Delereue C, de Franceschi S and Sanquer M 2014 Phys. Rev. B 89 161404 [29] Verduijn J, Tettamanzi G C and Rogge S 2013 Nano Lett. 13 1476 [30] Efros A L and Shklovskii B I 1975 J. Phys. C: Solid State Phys. 8 L49 [31] Oh J H, Ahn D, Yu Y S and Hwang S W 2008 Phys. Rev. B 77 035313
[32] Kohn W and Luttinger J M 1955 Phys. Rev. 98 915 [33] Aggarwal R L and Ramdas A K 1965 Phys. Rev. 140 A1246 [34] Diarra M, Niquet Y-M, Delerue C and Allan G 2007 Phys. Rev. B 75 045301 [35] Hao Y L, Djotyan A P, Avetisyan A A and Peeters F M 2009 Phys. Rev. B 80 035329 [36] Calderon M J, Verduijn J, Lansbergen G P, Tettamanzi G C, Rogge S and Koiller B 2010 Phys. Rev. B 82 075317 [37] Saraiva A L, Koiller B and Friesen M 2010 Phys. Rev. B 82 245314 [38] Shevchenko S, Ashhab S and Nori F 2010 Phys. Rep. 492 1 [39] Stoof T H and Nazarov Y V 1996 Phys. Rev. B 53 1050 [40] Hayashi T, Fujisawa T, Cheong H D, Jeong Y H and Hirayama Y 2003 Phys. Rev. Lett. 91 226804 [41] Petta J R, Johnson A C, Marcus C M, Hanson M P and Gossard A C 2004 Phys. Rev. Lett. 93 186802 [42] Roche B, Riwar R-P, Voisin B, Dupont-Ferrier E, Wacquez R, Vinet M, Sanquer M, Splettstoesser J and Jehl X 2013 Nat. Commun. 4 1581 [43] Weber B, Tan Y H M, Mahapatra S, Watson T F, Ryu H, Rahman R, Hollenberg L C L, Klimeck G and Simmons M Y 2014 Nat. Nano. 9 430 [44] Clapera P et al unpublished
8
