We present an electrostatically defined few-electron double quantum dot (QD) realized in a molecular beam epitaxy grown Si/SiGe heterostructure. Transport and charge spectroscopy with an additional QD as well as pulsed-gate measurements are demonstrated. We discuss technological challenges specific for silicon-based heterostructures and the effect of a comparably large effective electron mass on transport properties and tunability of the double QD. Charge noise, which might be intrinsically induced due to strain-engineering is proven not to affect the stable operation of our device as a spin qubit. Our results promise the suitability of electrostatically defined QDs in Si/SiGe heterostructures for quantum information processing.
We perform quantum Hall measurements on three types of commercially available modulation doped Si/SiGe heterostructures to determine their suitability for depletion gate defined quantum dot devices. By adjusting the growth parameters, we are able to achieve electron gases with charge densities 1-3 X 10^{11}/cm^2 and mobilities in excess of 100,000 cm^2/Vs. Double quantum dot devices fabricated on these heterostructures show clear evidence of single charge transitions as measured in dc transport and charge sensing and exhibit electron temperatures of 100 mK in the single quantum dot regime.
We perform detailed magnetotransport studies on two-dimensional electron gases (2DEGs) formed in undoped Si/SiGe heterostructures in order to identify the electron mobility limiting mechanisms in this increasingly important materials system. By analyzing data from 26 wafers with different heterostructure growth profiles we observe a strong correlation between the background oxygen concentration in the Si quantum well and the maximum mobility. The highest quality wafer supports a 2DEG with a mobility of 160,000 cm^2/Vs at a density 2.17 x 10^11/cm^2 and exhibits a metal-to-insulator transition …
Spin splitting of conduction electron states has been analyzed for all possible point symmetries of SiGe quantum well structures. A particular attention is paid to removal of spin degeneracy caused by the rotoinversion asymmetry of a (001) heterointerface between two diamond-lattice materials. Consequences of the spin splitting on the electron spin relaxation time is discussed.
Elastic strain distributions in SiGe heterostructures with quantum dots have been simulated with the use of the finite element method. The effect of a non-uniform germanium distribution in the nanoislands on the spatial dependence and the magnitude of elastic fields was studied. It is shown that quantum dots with a uniform component content are more strained in comparison with non-uniform nanoislands
The valley degree of freedom presents challenges and opportunities for silicon spin qubits. An important consideration for singlet-triplet states is the presence of two distinct triplets, comprised of valley vs. orbital excitations. Here we show that both of these triplets are present in the typical operating regime, but that only the valley-excited triplet offers intrinsic protection against charge noise. We further show that this protection arises naturally in dots with stronger confinement. These results reveal an inherent advantage for silicon-based multi-electron qubits.
A split gate technique is used to form a lateral quantum dot in a two-dimensional electron gas of a modulation-doped silicon/silicon-germanium heterostructure. e-beam lithography was employed to produce split gates. By applying negative voltages to these gates the underlying electron gas is depleted and a lateral quantum dot is formed, the size of which can be adjusted by the gate voltage. We observe single-electron operation with Coulomb blockade behavior below 1K. Gate leakage currents are well controlled, indicating that the recently encountered problems with Schottky gates for this type of…
Measurement results of the acoustoelectric effects (surface acoustic waves (SAW) attenuation and velocity) in a high-mobility $p$-SiGe/Ge/SiGe structure are presented. The structure was LEPECVD grown with a two dimensional (2D) channel buried in the strained Ge layer. The measurements were performed as a function of temperature (1.5 - 4.2 K) and magnetic field (up to 8.4 T) at different SAW intensities at frequencies 28 and 87 MHz. Shubnikov-de Haas-like oscillations of both SAW attenuation and the velocity change have been observed. Hole density and mobility, effective mass, quantum and trans…
The contactless Surface Acoustic Wave (SAW) technique was implemented to probe the high-frequency (ac) conductivity in a high-mobility $p$-SiGe/Ge/SiGe structure in the integer quantum Hall (IQHE) regime. The structure was grown by low-energy plasma-enhanced chemical vapor deposition and comprised a two-dimensional channel formed in a compressively strained Ge layer. It was investigated at temperatures of 0.3 - 5.8 K and magnetic fields up to 18 T at various SAW intensities. In the IQHE regime, in minima of the conductivity oscillations with small filling factors, holes are localized. The ac c…
Spin and valley-orbit splittings are calculated in SiGe/Si/SiGe quantum wells (QWs) by using the tight-binding approach. In accordance with the symmetry considerations an existence of spin splitting of electronic states in perfect QWs with an odd number of Si atomic planes is microscopically demonstrated. The spin splitting oscillates with QW width and these oscillations related to the inter-valley reflection of an electron wave from the interfaces. It is shown that the splittings under study can efficiently be described by an extended envelope-function approach taking into account the spin- a…
In the present work we have investigated the transport properties in a number of Si/SiGe samples with square antidot lattices of different periods. In samples with lattice periods equal to 700 nm and 850 nm we have observed the conventional low-field commensurability magnetoresistance peaks consistent with the previous observations in GaAs/AlGaAs and Si/SiGe samples with antidot lattices. In samples with a 600 nm lattice period a new series of well-developed magnetoresistance oscillations has been found beyond the last commensurability peak which are supposed to originate from periodic skippin…
Silicon-germanium heterostructures have successfully hosted quantum dot qubits, but the intrinsic near-degeneracy of the two lowest valley states poses an obstacle to high fidelity quantum computing. We present a modification to the Si/SiGe heterostructure by the inclusion of a spike in germanium concentration within the quantum well in order to increase the valley splitting. The heterostructure is grown by chemical vapor deposition and magnetospectroscopy is performed on gate-defined quantum dots to measure the excited state spectrum. We demonstrate a large and widely tunable valley splitting…
The surface acoustic wave (SAWs) attenuation coefficient $Γ$ and the velocity change $ΔV /V$ were measured for $p$-type Si/SiGe heterostructures in the temperature range 0.7 - 1.6 K as a function of external magnetic field $H$ up to 7 T and in the frequency range 30-300 MHz in the hole Si/SiGe heterostructures. Oscillations of $Γ$ (H) and $ΔV /V$ (H) in a magnetic field were observed. Both real $σ_1$ (H) and imaginary $σ_2$ (H) components of the high-frequency conductivity have been determined. Analysis of the $σ_1$ to $σ_2$ ratio allows the carrier localization to be followed as a function of…
It is shown that recent and earlier experiments, which claimed to observe a disagreement with the global phase diagram (GPD) of the quantum Hall effect, do not, in fact, contradict the GPD. Two aspects should be taken into account: (i) insulating phases between quantum Hall phases are possible owing to the Shubnikov-de Haas oscillations of the "bare" diagonal resistivity $ρ_{xx}^{0}$; (ii) according to the two-parameter scaling theory, the filling factor $ν$ does not determine directly the positions of the quantum Hall phases on the magnetic field axis at $ω_{c}τ\lesssim 1$.
We study DC and AC transport in low-density $p-$Si/SiGe heterostructures at low temperatures and in a broad domain of magnetic fields up to 18 T. Complex AC conductance is determined from simultaneous measurement of velocity and attenuation of a surface acoustic wave propagating in close vicinity of the 2D hole layer. The observed behaviors of DC and AC conductance are interpreted as an evolution from metallic conductance at B=0 through hopping between localized states in intermediate magnetic fields (close to the plateau of the integer quantum Hall effect corresponding to the Landau-level fil…
We show that Ge concentration oscillations within the quantum well region of a Si/SiGe heterostructure can significantly enhance the spin-orbit coupling of the low-energy conduction-band valleys. Specifically, we find that for Ge oscillation wavelengths near $λ= 1.57~\text{nm}$ with an average Ge concentration of $\bar{n}_{\text{Ge}} = 5\%$ in the quantum well region, a Dresselhaus spin-orbit coupling is induced, at all physically relevant electric field strengths, which is over an order of magnitude larger than what is found in conventional Si/SiGe heterostructures without Ge concentration os…
We report on the realization and top-gating of a two-dimensional electron system in a nuclear spin free environment using 28Si and 70Ge source material in molecular beam epitaxy. Electron spin decoherence is expected to be minimized in nuclear spin-free materials, making them promising hosts for solid-state based quantum information processing devices. The two-dimensional electron system exhibits a mobility of 18000 cm2/Vs at a sheet carrier density of 4.6E11 cm-2 at low temperatures. Feasibility of reliable gating is demonstrated by transport through split-gate structures realized with pallad…
We have investigated temperature dependence of the longitudinal conductivity $σ_{xx}$ at integer filling factors $ν=i$ for Si/SiGe heterostructure in the quantum Hall effect regime. It is shown that for odd $i$, when the Fermi level $E_{F}$ is situated between the valley-split levels, $Δσ_{xx}$ is determined by quantum corrections to conductivity caused by the electron-electron interaction: $Δσ_{xx}(T)\sim \ln T$. For even $i$, when $E_{F}$ is located between cyclotron-split levels or spin-split levels, $σ_{xx}\sim \exp[-Δ_{i}/T]$ for $i=6,10,12$ and $\sim \exp [-(T_{0i}/T)]^{1/2}$ for $i=4,8$…
Small spin-qubit registers defined by single electrons confined in Si/SiGe quantum dots operate successfully and connecting these would permit scalable quantum computation. Shuttling the qubit carrying electrons between registers is a natural choice for high-fidelity coherent links provided the overhead of control signals stays moderate. Our proof-of-principle demonstrates shuttling of a single electron by a propagating wave-potential in an electrostatically defined 420 nm long Si/SiGe quantum-channel. This conveyor-mode shuttling approach requires independent from its length only four sinusoi…
The magnetoresistance components $ρ_{xx}$ and $ρ_{xy}$ were measured in two p-Si/SiGe/Si quantum wells that have an anisotropic g-factor in a tilted magnetic field as a function of temperature, field and tilt angle. Activation energy measurements demonstrate the existence of a ferromagnetic-paramagnetic (F-P) transition for a sample with a hole density of $p$=2$\times10^{11}$\,cm$^{-2}$. This transition is due to crossing of the 0$\uparrow$ and 1$\downarrow$ Landau levels. However, in another sample, with $p$=7.2$\times10^{10}$\,cm$^{-2}$, the 0$\uparrow$ and 1$\downarrow$ Landau levels coinci…
Optimization of Si/SiGe Heterostructures for Large and Robust Valley Splitting in Silicon Qubits
Weierstrass Institute for Applied Analysis and Stochastics (WIAS)（魏茨塞克应用分析与随机过程研究所）；RWTH Aachen University（亚琛工业大学）；Forschungszentrum Jülich（于利希研究中心）；Institute of Quantum Information（量子信息研究所）；ARQUE Systems GmbH（ARQUE系统有限公司）
We report low-temperature magneto-transport measurements of an undoped Si/SiGe asymmetric double quantum well heterostructure. The density in both layers is tuned independently utilizing a top and a bottom gate, allowing the investigation of quantum wells at both imbalanced and matched densities. Integer quantum Hall states at total filling factor $ν_{\text{T}} = 1$ and $ν_{\text{T}} = 2$ are observed in both density regimes, and the evolution of their excitation gaps is reported as a function of density. The $ν_{\text{T}} = 1$ gap evolution departs from the behavior generally observed for val…
We have investigated the valley splitting of two-dimensional electrons in high quality Si/Si$_{1-x}$Ge$_x$ heterostructures under tilted magnetic fields. For all the samples in our study, the valley splitting at filling factor $ν=3$ ($Δ_3$) is significantly different before and after the coincidence angle, at which energy levels cross at the Fermi level. On both sides of the coincidence, a linear density dependence of $Δ_3$ on the electron density was observed, while the slope of these two configurations differs by more than a factor of two. We argue that screening of the Coulomb interaction f…
We present a unified approach for calculating the properties of shallow donors inside or outside heterostructure quantum wells. The method allows us to obtain not only the binding energies of all localized states of any symmetry, but also the energy width of the resonant states which may appear when a localized state becomes degenerate with the continuous quantum well subbands. The approach is non-variational, and we are therefore also able to evaluate the wave functions. This is used to calculate the optical absorption spectrum, which is strongly non-isotropic due to the selection rules. The …
The electron transport in the two-dimensional gas formed in tensile-strained Si1-xGex/Si/Si1-xGex heterostructures is investigated using Monte Carlo simulation. At first the electron mobility is studied in ungated modulation doped structures. The calculation matches very well the experimental results over a wide range of electron density. The mobility typically varies between 1100 cm2/Vs in highly-doped structures and 2800 cm2/Vs at low electron density. The mobility is shown to be significantly influenced by the thickness of the spacer layer separating the strained Si channel from the pulse-d…
Silicon-Germanium (SiGe) is a material that possesses a multitude of applications ranging from transistors to eletro-optical modulators and quantum dots. The diverse properties of SiGe also make it attractive to implementations involving superconducting quantum computing. Here we demonstrate the fabrication of transmon quantum bits on SiGe layers and investigate the microwave loss properties of SiGe at cryogenic temperatures and single photon microwave powers. We find relaxation times of up to 100 $μ$s, corresponding to a quality factor Q above 4 M for large pad transmons. The high Q values ob…
We report the fabrication and characterization of a gate-defined double quantum dot formed in a Si/SiGe nanomembrane. In the past, all gate-defined quantum dots in Si/SiGe heterostructures were formed on top of strain-graded virtual substrates. The strain grading process necessarily introduces misfit dislocations into a heterostructure, and these defects introduce lateral strain inhomogeneities, mosaic tilt, and threading dislocations. The use of a SiGe nanomembrane as the virtual substrate enables the strain relaxation to be entirely elastic, eliminating the need for misfit dislocations. Howe…
Interactions between electrons can strongly affect the shape and functionality of multi-electron quantum dots. The resulting charge distributions can be localized, as in the case of Wigner molecules, with consequences for the energy spectrum and tunneling to states outside the dot. The situation is even more complicated for silicon dots, due to the interplay between valley, orbital, and interaction energy scales. Here, we study two-electron wavefunctions in electrostatically confined quantum dots formed in a SiGe/Si/SiGe quantum well at zero magnetic field, using a combination of tight-binding…
We report the observation of the quantum-confined Stark effect in Ge/SiGe multiple quantum well heterostructures grown on Si(0.22)Ge(0.78) virtual substrates. The large compressive strain in the Ge quantum well layers caused by the lattice mismatch with the virtual substrate results in a blue shift of the direct absorption edge, as well as a reduction in the Γ-valley scattering lifetime because of strain-induced splittings of the conduction band valleys. We investigate theoretically the Γ-valley carrier lifetimes by evaluating the Γ-to-L and Γ-to-Δ scattering rates in strained Ge/SiGe semicond…
Optically programmable and erasable cryogenic flash memory on an undoped Si/SiGe heterostructure
Center for Research in Nanotechnology and Science, Indian Institute of Technology Bombay（印度孟买理工学院纳米科学与技术研究中心）；Department of Physics, Indian Institute of Technology Bombay（印度孟买理工学院物理系）；QuTech and Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学QuTech和卡弗里纳米科学研究所）；Centre of Excellence in Quantum Information, Computing, Science & Technology, IIT Bombay（印度孟买理工学院量子信息、计算、科学与技术卓越中心）
We report the observation of a metal-insulator transition (MIT) in a two- dimensional electron gas (2DEG) in a Si/SiGe heterostructure at zero magnetic field. On going through the MIT we observe the corresponding evolution of the magnetic field induced transition between the insulating phase and the quantum Hall (QH) liquid state in the QH regime. Similar to the previous reports for a GaAs sample, we find that the critical magnetic field needed to produce the transition becomes zero at the critical electron density corresponding to the zero field MIT. The temperature dependence of the conducti…
We fabricated strongly confined Schottky-gated quantum point contacts by etching Si/SiGe heterostructures and observed intriguing conductance quantization in units of approximately 1e2/h. Non-linear conductance measurements were performed depleting the quantum point contacts at fixed mode-energy separation. We report evidences of the formation of a half 1e2/h plateau, supporting the speculation that adiabatic transmission occurs through 1D modes with complete removal of valley and spin degeneracies.
We study double quantum dots in a Ge/SiGe heterostructure and test their maturity towards singlet-triplet ($S-T_0$) qubits. We demonstrate a large range of tunability, from two single quantum dots to a double quantum dot. We measure Pauli spin blockade and study the anisotropy of the $g$-factor. We use an adjacent quantum dot for sensing charge transitions in the double quantum dot at interest. In conclusion, Ge/SiGe possesses all ingredients necessary for building a singlet-triplet qubit.
We report the observation of an electron gas in a SiGe/Si/SiGe quantum well with maximum mobility up to 240 m^2/Vs, which is noticeably higher than previously reported results in silicon-based structures. Using SiO, rather than Al_2O_3, as an insulator, we obtain strongly reduced threshold voltages close to zero. In addition to the predominantly small-angle scattering well known in the high-mobility heterostructures, the observed linear temperature dependence of the conductivity reveals the presence of a short-range random potential.
We grow $^{28}$Si/SiGe heterostructures by reduced-pressure chemical vapor deposition and terminate the stack without an epitaxial Si cap but with an amorphous Si-rich layer obtained by exposing the SiGe barrier to dichlorosilane at 500 °C. As a result, $^{28}$Si/SiGe heterostructure field-effect transistors feature a sharp semiconductor/dielectric interface and support a two-dimensional electron gas with enhanced and more uniform transport properties across a 100 mm wafer. At T = 1.7 K we measure a high mean mobility of (1.8$\pm$0.5)$\times$10$^5$ cm$^2$/Vs and a low mean percolation density …
