This paper presents a detailed fabrication protocol for gate-defined semiconductor lateral quantum dots on gallium arsenide heterostructures. These nanoscale devices are used to trap few electrons for use as quantum bits in quantum information processing or for other mesoscopic experiments such as coherent conductance measurements.
A quantum computer is a computer composed of quantum bits (qubits) that takes advantage of quantum effects, such as superposition of states and entanglement, to solve certain problems exponentially faster than with the best known algorithms on a classical computer. Gate-defined lateral quantum dots on GaAs/AlGaAs are one of many avenues explored for the implementation of a qubit. When properly fabricated, such a device is able to trap a small number of electrons in a certain region of space. The spin states of these electrons can then be used to implement the logical 0 and 1 of the quantum bit. Given the nanometer scale of these quantum dots, cleanroom facilities offering specialized equipment- such as scanning electron microscopes and e-beam evaporators- are required for their fabrication. Great care must be taken throughout the fabrication process to maintain cleanliness of the sample surface and to avoid damaging the fragile gates of the structure. This paper presents the detailed fabrication protocol of gate-defined lateral quantum dots from the wafer to a working device. Characterization methods and representative results are also briefly discussed. Although this paper concentrates on double quantum dots, the fabrication process remains the same for single or triple dots or even arrays of quantum dots. Moreover, the protocol can be adapted to fabricate lateral quantum dots on other substrates, such as Si/SiGe.
Quantum information science has drawn a lot of attention ever since it was shown that quantum algorithms can be used to solve certain problems exponentially faster than with the best known classical algorithms1. An obvious candidate for a quantum bit (qubit) is the spin of single electron confined in a quantum dot since it is a two-level system. Numerous architectures have been suggested for the implementation of quantum dots, including semiconducting nanowires2, carbon nanotubes3, self-assembled quantum dots4, and semiconductor vertical5 and lateral quantum dots6. Gate-defined lateral quantum dots in GaAs/AlGaAs heterostructures have been very successful because of their versatility and their fabrication process is the focus of this paper.
In lateral quantum dots, the confinement of electrons in the direction perpendicular to the sample surface (z direction) is achieved by choosing the proper substrate. The GaAs/AlGaAs modulation-doped heterostructure presents a two-dimensional electron gas (2DEG) confined to the interface between the AlGaAs and the GaAs layers. These samples are grown by molecular beam epitaxy to obtain a low impurity density which, combined with the modulation-doping technique, leads to high electron mobility in the 2DEG. A schematic of the different layers of the heterostructure as well as its band structure are shown in Figure 1. A high electron mobility is needed in the 2DEG to ensure the coherence of electronic states over the entire surface of the quantum dot. The substrate used for the fabrication process described below was purchased from the National Research Council of Canada and presents an electron density of 2.2 x 1011cm-2 and an electron mobility of 1.69 x 106 cm2/Vsec.
The confinement of electrons in the directions parallel to the sample surface is achieved by placing metallic electrodes on the surface of the substrate. When these electrodes are deposited on the surface of the GaAs sample, Schottky barriers are formed7. Negative voltages applied to such electrodes lead to local barriers in the 2DEG below which only electrons with sufficient energy can cross. Depletion of the 2DEG occurs when the voltage applied is negative enough that no electrons have enough energy to cross the barrier. Therefore, by carefully choosing the geometry of the electrodes, it is possible to trap a small number of electrons between depleted regions of the sample. Control of the number of electrons on the dot as well as the tunneling energy between the dot and the 2DEG in the rest of the sample can be achieved by fine-tuning the voltages on the electrodes. A schematic of the gate electrodes and the depleted electron gas is shown in Figure 2. The design for the gate structures forming the dot is inspired by the design used by Barthel et al.8
To control and read out information regarding the number of electrons on the dot, it is useful to induce and measure current through the dot. Readout can also be done by using a Quantum Point Contact (QPC), which also requires a current through the 2DEG. The contact between the 2DEG and voltage sources is ensured by ohmic contacts. These are metallic pads that are diffused from the surface of the sample all the way down to the 2DEG using a standard rapid thermal anneal process7 (see Figures 3a and 4b). To avoid short circuits between the source and the drain, the surface of the sample is etched so that the 2DEG is depleted in certain regions and the current is forced to travel through certain specific channels (see Figures 3b and 4a). The region where the 2DEG still remains is referred to as the "mesa".
The following protocol details the entire fabrication process of a gate-defined lateral quantum dot on a GaAs/AlGaAs substrate. The process is scalable since it remains the same regardless if the device being fabricated is a single, double, or triple quantum dot or even an array of quantum dots. Manipulation, measurement, and results for double quantum dots fabricated using this method are discussed in further sections.
The fabrication process described below is done on a GaAs/AlGaAs substrate with dimensions of 1.04 x 1.04 cm. Twenty identical devices are fabricated on a substrate of this size. All steps of the process are done in a cleanroom and appropriate protective gear must be used at all times. Deionized water is used throughout the process, but is simply referred to as "water" in the protocol below.
1. Etching of the Mesa
The result of this fabrication step is shown in Figure 4a.
2. Fabrication of the Ohmic Contacts
The result of this fabrication step is shown in Figure 4b.
3. Fabrication of the Ti/Au Schottky Leads
The result of this fabrication step is shown in Figure 4c.
4. Fabrication of the Al Schottky Leads and Gates
The result of this fabrication step is shown in Figure 4d.
The fabrication of the Al Schottky leads and gates constitutes the most critical step of the fabrication process since these are the gates that define the dot. It is important that the electron beam be well focused and the beam current well adjusted in step 4.2. The exposure and development times must also be well adjusted to obtain small, continuous and well-defined gates. In many protocols, these gates and leads are fabricated in Ti/Au and are exposed simultaneously with the previous leads during step 3. However, an advantage of using Al is that it can be oxidized, therefore allowing for elements such as top gates to be deposited directly onto the surface of the sample without the need of a large insulating layer10.
5. Fabrication of the Schottky Leads and Bonding Pads
The result of this fabrication step is shown in Figure 4e.
6. Dicing of the Samples
One of the critical steps in the process described above is the etching of the mesa (step 1). It is important to etch enough to remove the 2DEG below while avoiding overetching. Therefore, it is recommended to use a bulk GaAs dummy sample to test the etching solution before performing the etch on the GaAs/AlGaAs sample. The etch rate of the GaAs/AlGaAs heterostructure is larger than that of GaAs, but the etching of the dummy can give an indication to whether the solution is more or less reactive than usual and the etch time of the actual sample can be adjusted accordingly.
Once the devices have been fabricated, they are ready to be attached to a sample holder using silver epoxy. Wire bonding between the sample's bonding pads and the sample holder's connection pins is done using 25 μm Al wire. It is best to avoid observing the devices in a Scanning Electron Microscope (SEM) because there is a risk of damaging them. Instead, there are simple tests that can be done at fairly high temperatures (~4 K) and that allow to confirm if any of the gates are broken or missing before cooling the sample in a dilution refrigerator for further characterization. One of these tests consists in applying a voltage bias between two ohmic contacts and measuring the current driven through the sample as a function of the voltage applied on a pair of gates. An example of such measurements is shown in Figure 5. The curves in Figure 5 show two distinct regimes. The first regime ranges from 0 V to -750 mV and presents two depletion steps: one at about -300mV corresponding to the depletion of the 200 nm wide leads and one at about -750mV corresponding to the depletion of the 60 nm wide gates. The second regime at lower voltages shows plateaus that correspond to the quantization of the conductance. Typical values for pinch-off points between pairs of gates range between -500mV to -2V. Moreover, one shouldn't apply positive voltage above 500 or 600 mV on a gate since it could damage the Schottky barrier. From Figure 5, it is possible to conclude that, in the case of this particular sample, the gates are likely to be geometrically similar since the TC-TL and TC-TR pairs pinch off the current at approximately equal voltages. The same goes for the TC-BL and TC-BR pairs. However, the fact that the current still flows between the TC and BC gates even for high voltages indicates that the BC gate is either broken or missing. Usually, about 50% of the tested devices have fully functional gates and ohmic contacts.
Once a suitable device has been found, it can be loaded into a dilution refrigerator for characterization at low temperatures (<100 mK). The voltages on each of the gates must then be adjusted to form the double dot. It is not the goal of this paper to detail this adjustment process. Once a double dot has been formed, a stability diagram can be measured to check if the double dot can reach the few-electron regime. This is done by applying a small constant source-drain bias (~10 μV) and by measuring the current through the double dot as a function of the voltages applied on the BL and BR gates. If the design of the device includes a quantum point contact which serves as a charge detector, it is preferable to use this, rather than the current through the dot, for the measurement of the stability diagram11. A measured stability diagram and a schematic of an ideal result are shown in Figure 6. As shown in Figure 6b, current only flows through the double dot at triple points. The zero-electron regime is reached when no more triple points can be observed in the stability diagram, no matter how negative the voltages on the gates become. However, the fact that current no longer flows through the dot for high voltages can also indicate that the tunnel barriers connecting the source and drain to the double dot have been completely pinched off. Spin blockade can be measured at different triple points to prove that the few-electron regime has been reached12, but the exact number of electrons in the double dot needs to be determined using charge sensing. For more detailed information regarding stability diagrams, spin blockade and charge sensing see R. Hanson et al.13
Figure 1. a) Sequence of layers present in a GaAs/AlGaAs heterostructure grown by molecular beam epitaxy. b) Band structure of the heterostructure shown in a). Bc and Bv are respectively the conduction and valence bands. The only region where the conduction band is below the Fermi level (Ef) is found between the 5,000 Å layer of GaAs and the 400 Å layer of AlGaAs. It is here that the 2DEG is found. Click here to view larger image.
Figure 2. Schematic of the metallic gate electrodes (dark grey) of a double quantum dot deposited on top of a GaAs/AlGaAs heterostructure. The 2DEG is shown in orange and the depleted regions are white. The black squares represent ohmic contacts and the arrows show the current flow through the dot and the quantum point contact (QPC). The two dots are located in the orange regions where electrons still remain in the center of the depleted zone. Gates BL and BR are used to control the number of electrons on the left and right dots respectively. BC and TC control the tunnel barrier between the two dots. TL is used to tune the tunnel barrier between the source and the left dot while TR tunes the barrier between the right dot and the drain. Click here to view larger image.
Figure 3. (a) Schematic of a Ni/Ge/Au ohmic contact (golden rectangles) diffused by rapid thermal anneal from the surface of the sample down to the 2DEG. (b) Lateral view of the surface of the sample that is etched to create the mesa. Click here to view larger image.
Figure 4. Optical microscope images of a double quantum dot device after different steps of the fabrication process. (a) Device after the etching of the mesa (step 1). The light gray areas have been etched away preventing the electric current from flowing through these regions, while the dark gray regions still present a 2DEG. (b) Device after the fabrication of the ohmic contacts (step 2). The ohmic contacts are the gold squares. (c) Device after the fabrication of the Ti/Au Schottky leads (step 3). The leads are the white lines in the center of the image. (d) Device after the fabrication of the Al Schottky leads and gates (step 4). These are found in the green square in the center of the image. A SEM image of the gates used to define the quantum dots is also shown. (e) Device after the fabrication of the Schottky leads and bonding pads (step 5). Click here to view larger image.
Figure 5. Current flowing from source to drain as a function of the voltage applied on different pairs of gates. The depletion of the electron gas begins at ~-400 mV and is finished at ~-700 mV. The voltage bias applied between the source and the drain is 500 μV and the current is measured by a two-point measurement. All curves are taken at 1.4 K. Click here to view larger image.
Figure 6. (a) Schematic of an ideal stability diagram that would be obtained using a QPC. Lines can be observed when an electron tunnels onto one dot or between the dots. The black circles represent triple points where it is possible for current to flow through the dot. (b) Stability diagram obtained by measuring the current flowing through the dot with TL = -100 mV, TC = -350 mV, TR = -1,080 mV, BC = -1,160 mV, QPC = -600 mV and a source-drain bias of 10 μV. The sample was bias-cooled with a voltage V = +500 mV on each gate, which shifts all the depletion and pinch-off points by approximately 500 mV and reduces telegraphic noise in the experiment14. For this type of stability diagram, only the triple points are supposed to be visible, as is the case here for the most negative voltages. In both (a) and (b), the numbers (L,R) indicate the number of electrons in the left and right dot for different values of the voltages on the BL and BR gates. The green lines in (b) are guides to show the regions with a constant number of electrons. Click here to view larger image.
The process presented above describes the fabrication protocol of a double quantum dot able to reach the few-electron regime. However, the parameters given may vary depending on the model and calibration of the equipment used. Therefore, parameters such as the doses for exposures during the e-beam and photolithography steps will have to be calibrated before the fabrication of devices. The process can easily be adapted to the fabrication of gate-defined quantum dots on other types of substrates, such as Si/SiGe, that also present a 2DEG.
For certain types of devices, such as vertical quantum dots, the tunnel barrier from the source and the drain to the dot are determined during fabrication and cannot be varied afterward5. An advantage of gate-defined lateral quantum dots is that the tunnel barriers to the dot as well as between the dots can be controlled electrically. However, because of this, care must be taken to maintain these values during the manipulation of the voltages on the other gates defining the dot.
It is important to remember that, once the few-electron regime has been reached, the goal is to manipulate the spin states of the electrons on the dot to perform quantum calculations. The 0 and 1 states of the qubit have been successfully implemented in the up and down spin states of a single electron15 as well as in the S-T016 and S-T+17 states of two spins. Coupling between two qubits has also been achieved using these devices18. However, one of the major drawbacks of lateral quantum dots in GaAs/AlGaAs is the short coherence time (the time during which the spin state of the electrons in the dot is preserved) caused by interaction with the nuclear spins of the atoms forming the substrate19. This has led to the investigation of lateral quantum dots in materials such as silicon (Si/SiGe heterostructures20) and carbon (graphene21) that have isotopes that are free of nuclear spin and are expected to lead to theoretically long coherence times. However, these devices have yet to achieve the results of control and read-out obtained for dots in GaAs/AlGaAs. Current work involving GaAs/AlGaAs double quantum dots also includes coupling of the device to a microwave resonator22 and the integration of micromagnets to allow faster spin operations23.
The authors have nothing to disclose.
The authors thank Michael Lacerte for technical support. M.P.-L. acknowledges the Canadian Institute for Advanced Research (CIFAR), the Natural Sciences and Engineering Research Council of Canada (NSERC), the Canadian Foundation for Innovations (CFI) and Fonds de Recherche Québec – Nature et Technologies (FRQNT) for financial support. The device presented here was fabricated at CRN2 and IMDQ facilities, funded in part by NanoQuébec. The GaAs/AlGaAs substrate was fabricated by Z.R. Wasilewski from the Institute of Microstructural Sciences at the National Research Council Canada. J.C.L and C.B.-O. acknowledge CRSNG and FRQNT for financial support.
Name of the reagent/material | Company | Product number | CAS number |
Acetone – CH3COCH3 | Anachemia | AC-0150 | 67-64-1 |
Isopropyl Alcohol (IPA) – (CH3)2CHOH | Anachemia | AC-7830 | 67-63-0 |
1165 Remover | MicroChem Corp | G050200 | 872-50-4 |
Microposit MF-319 Developer | Shipley | 38460 | 75-59-2 |
Sulfuric Acid – H2SO4 | Anachemia | AC-8750 | 766-93-9 |
Hydrogen Peroxide (30%) – H2O2 | Fisher Scientific | 7722-84-1 | |
LOR 5A Lift-off resist | MicroChem Corp | G516608 | 120-92-3 |
Microposit S1813 Photo Resist | Shipley | 41280 | 108-65-6 |
Microposit S1818 Photo Resist | Shipley | 41340 | 108-65-6 |
PMMA LMW 4% in anisole | MicroChem Corp | 100-66-3, 9011-14-7 | |
PMMA HMW 2% in anisole | MicroChem Corp | 100-66-3, 9011-14-7 | |
GaAs/AlGaAs wafer | National Research Council Canada | See detailed layer structure in Figure 1. | |
Ni (99.0%) | Anachemia | ||
Ge (99.999%) | CERAC inc. | ||
Au (99.999%) | Kamis inc. | ||
Ti (99.995%) | Kurt J Lesker | ||
Al | Kamis inc. | ||
Silver Epoxy | Epoxy Technology | H20E |