We report density-dependent effective hole mass measurements in undoped germanium quantum wells. We are able to span a large range of densities ($2.0-11\times10^{11}$ cm$^{-2}$) in top-gated field effect transistors by positioning the strained buried Ge channel at different depths of 12 and 44 nm from the surface. From the thermal damping of the amplitude of Shubnikov-de Haas oscillations, we measure a light mass of $0.061m_e$ at a density of $2.2\times10^{11}$ cm$^{-2}$. We confirm the theoretically predicted dependence of increasing mass with density and by extrapolation we find an effective mass of $\sim0.05m_e$ at zero density, the lightest effective mass for a planar platform that demonstrated spin qubits in quantum dots.
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 …
We demonstrate double quantum dots fabricated in undoped Si/SiGe heterostructures relying on a double top-gated design. Charge sensing shows that we can reliably deplete these devices to zero charge occupancy. Measurements and simulations confirm that the energetics are determined by the gate-induced electrostatic potentials. Pauli spin blockade has been observed via transport through the double dot in the two electron configuration, a critical step in performing coherent spin manipulations in Si.
We develop quantum dots in a single layered MOS structure using an undoped Si/SiGe wafer. By applying a positive bias on the surface gates, electrons are accumulated in the Si channel. Clear Coulomb diamond and double dot charge stability diagrams are measured. The temporal fluctuation of the current is traced, to which we apply the Fourier transform analysis. The power spectrum of the noise signal is inversely proportional to the frequency, and is different from the inversely quadratic behavior known for quantum dots made in doped wafers. Our results indicate that the source of charge noise f…
We report on a quantum dot device design that combines the low disorder properties of undoped SiGe heterostructure materials with an overlapping gate stack in which each electrostatic gate has a dominant and unique function -- control of individual quantum dot occupancies and of lateral tunneling into and between dots. Control of the tunneling rate between a dot and an electron bath is demonstrated over more than nine orders of magnitude and independently confirmed by direct measurement within the bandwidth of our amplifiers. The inter-dot tunnel coupling at the (0,2)<-->(1,1) charge configura…
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…
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）
Even as today's most prominent spin-based qubit technologies are maturing in terms of capability and sophistication, there is growing interest in exploring alternate material platforms that may provide advantages, such as enhanced qubit control, longer coherence times, and improved extensibility. Recent advances in heterostructure material growth have opened new possibilities for employing hole spins in semiconductors for qubit applications. Undoped, strained Ge/SiGe quantum wells are promising candidate hosts for hole spin-based qubits due to their low disorder, large intrinsic spin-orbit cou…
We analyze spin splitting of the two-dimensional hole spectrum in strained asymmetric SiGe quantum wells (QWs). Based on the Luttinger Hamiltonian, we obtain expressions for the spin-splitting parameters up to the third order in the in-plane hole wavevector. The biaxial strain of SiGe QWs is found to be a key parameter that controls spin splitting. Application to SiGe field-effect transistor structures indicates that typical spin splitting at room temperature varies from a few tenth of meV in the case of Si QW channels to several meV for the Ge counterparts, and can be modified efficiently by …
In this letter we not only show improvement in the performance but also in the reliability of 30nm thick biaxially strained SiGe (20%Ge) channel on Si p-MOSFETs. Compared to Si channel, strained SiGe channel allows larger hole mobility (μh) in the transport direction and alleviates charge flow towards the gate oxide. μh enhancement by 40% in SiGe and 100% in Si-cap SiGe is observed compared to the Si hole universal mobility. A ~40% reduction in NBTI degradation, gate leakage and flicker noise (1/f) is observed which is attributed to a 4% increase in the hole-oxide barrier height (ϕ) in SiGe. S…
Enhancement-mode Si/SiGe electron quantum dots have been pursued extensively by many groups for \revEdit{their} potential in quantum computing. Most of the reported dot designs utilize multiple metal-gate layers and use Si/SiGe heterostructures with Ge concentration close to 30\%. Here we report the fabrication and low-temperature characterization of quantum dots in Si/Si$_{0.8}$Ge$_{0.2}$ heterostructures using only one metal-gate layer. We find that the threshold voltage of a channel narrower than 1 $μ$m increases as the width decreases. The higher threshold can be attributed to the combinat…
Quantum dot arrays are a versatile platform for the implementation of spin qubits, as high-bandwidth sensor dots can be integrated with single-, double- and triple-dot qubits yielding fast and high-fidelity qubit readout. However, for undoped silicon devices, reflectometry off sensor ohmics suffers from the finite resistivity of the two-dimensional electron gas (2DEG), and alternative readout methods are limited to measuring qubit capacitance, rather than qubit charge. By coupling a surface-mount resonant circuit to the plunger gate of a high-impedance sensor, we realized a fast charge sensing…
Quantum transport measurements are performed in gate-defined, high-quality, two-dimensional hole and electron systems in an undoped InSb quantum well. For both polarities, the carrier systems show tunable spin-orbit interaction as extracted from weak anti-localization measurements. The effective mass of InSb holes strongly increases with carrier density as determined from the temperature dependence of Shubnikov-de Haas oscillations. Coincidence measurements in a tilted magnetic field are performed to estimate the spin susceptibility of the InSb two-dimensional hole system. The g-factor of the …
Universal quantum computation requires high fidelity single qubit rotations and controlled two qubit gates. Along with high fidelity single qubit gates, strong efforts have been made in developing robust two qubit logic gates in electrically-gated quantum dot systems to realize a compact and nano-fabrication-compatible architecture. Here, we perform measurements of state-conditional coherent oscillations of a charge qubit. Using a quadruple quantum dot formed in a Si/SiGe heterostructure, we show the first demonstration of coherent two-axis control of a double quantum dot charge qubit in undop…
We implement a technique for measuring the singlet-triplet energy splitting responsible for spin-to-charge conversion in semiconductor quantum dots. This method, which requires fast, single-shot charge measurement, reliably extracts an energy in the limits of both large and small splittings. We perform this technique on an undoped, accumulation-mode Si/SiGe triple-quantum dot and find that the measured splitting varies smoothly as a function of confinement gate biases. Not only does this demonstration prove the value of having an $in~situ$ excited-state measurement technique as part of a stand…
We report on hole g-factor measurements in three terminal SiGe self-assembled quantum dot devices with a top gate electrode positioned very close to the nanostructure. Measurements of both the perpendicular as well as the parallel g-factor reveal significant changes for a small modulation of the top gate voltage. From the observed modulations we estimate that, for realistic experimental conditions, hole spins can be electrically manipulated with Rabi frequencies in the order of 100MHz. This work emphasises the potential of hole-based nano-devices for efficient spin manipulation by means of the…
The long-missing polarization-induced two-dimensional hole gas is finally observed in undoped gallium nitride quantum wells. Experimental results provide unambiguous proof that a 2D hole gas in GaN grown on AlN does not need acceptor doping, and can be formed entirely by the difference in the internal polarization fields across the semiconductor heterojunction. The measured 2D hole gas densities, about $4 \times 10^{13}$ cm$^{-2}$, are among the highest among all known semiconductors and remain unchanged down to cryogenic temperatures. Some of the lowest sheet resistances of all wide-bandgap s…
The spin-orbit interaction (SOI) of the two-dimensional hole gas in the inversion symmetric semiconductor Ge is studied in a strained-Ge/SiGe quantum well structure. We observed weak anti-localization (WAL) in the magnetoconductivity measurement, revealing that the WAL feature can be fully described by the k-cubic Rashba SOI theory. Furthermore, we demonstrated electric field control of the Rashba SOI. Our findings reveal that the heavy hole (HH) in strained-Ge is a purely cubic-Rashba-system, which is consistent with the spin angular momentum mj = +-3/2 nature of the HH wave function.
We have performed low-temperature transport experiments on a Si/SiGe hole system. The measured transverse and longitudinal condductivities $σ_{xx}$ and $σ_{xy}$ allow us to study the magnetic-field-induced transitions in the system. In particular, we present the first study of the temperature-driven flow lines in the "anomalous Hall insulator" regime near a Landau level filling factor $ν=1.5$. The "anomalous" temperature-driven flow lines could be due to the unusual energy level scheme in a Si/SiGe hole system. Moreover, for $3<ν<5$, there is a temperature-independent point in $ρ_{xx} (B)$, $ρ…
A single hole transistor is patterned in a p-Si/SiGe quantum well by applying voltages to nanostructured top gate electrodes. Gating is achieved by oxidizing the etched semiconductor surface and the mesa walls before evaporation of the top gates. Pronounced Coulomb blockade effects are observed at small coupling of the transistor island to source and drain.
The high-frequency (ac) conductivity of a high quality modulation doped GeSi/Ge/GeSi single quantum well structure with hole density $p$=6$\times$10$^{11}$cm$^{-2}$ was measured by the surface acoustic wave (SAW) technique at frequencies of 30 and 85~MHz and magnetic fields $B$ of up to 18 T in the temperature range of 0.3 -- 5.8 K. The acoustic effects were also measured as a function of the tilt angle of the magnetic field with respect to the normal of the two-dimensional channel at $T$=0.3 K. It is shown, that at the minima of the conductivity oscillations, holes are localized on the Fermi …
The existence of a metal-insulator transition at zero magnetic field in two- dimensional electron systems has recently been confirmed in high mobility Si-MOSFETs. In this work, the temperature dependence of the resistivity of gated Si/SiGe/Si quantum well structures has revealed a similar metal- insulator transition as a function of carrier density at zero magnetic field. We also report evidence for a Coulomb gap in the temperature dependence of the resistivity of the dilute 2D hole gas confined in a SiGe quantum well. In addition, the resistivity in the insulating phase scales with a single p…
Microwave-induced resistance oscillations (MIRO) have been extensively studied for more than a decade but, until now, have remained unique to GaAs/AlGaAs-based 2D electron systems. Here, we report on the first observation of MIRO in a 2D hole gas hosted in Ge/SiGe quantum well. Our findings confirm that MIRO is a universal phenomenon and demonstrate that microwave photoresistance can be utilized to probe the energy spectrum and the correlation effects of 2D holes in Ge/SiGe quantum wells.
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…
We find that temperature dependent screening can quantitatively explain the metallic behaviour of the resistivity on the metallic side of the so-called metal-insulator transition in p-SiGe. Interference and interaction effects exhibit the usual insulating behaviour which is expected to overpower the metallic background at sufficiently low temperatures. We find empirically that the concept of a Fermi-liquid describes our data in spite of the large r_s = 8.
Simultaneous study of acoustic and optic phonon scattering of electrons and holes in undoped $\mathrm{GaAs}$/$\mathrm{Al_{x} Ga_{1-x} As}$ heterostructures
本研究利用非掺杂 GaAs/AlGaAs 异质结构，通过电阻率温度依赖性测量，在 1.6-92.5K 范围内同步研究了二维电子和空穴的声学与光学声子散射，提取了耦合常数和 LO 激活能，验证了该方法的有效性。
We demonstrate a hole double quantum dot in an undoped GaAs/AlGaAs heterostructure. The interdot coupling can be tuned over a wide range, from formation of a large single dot to two well-isolated quantum dots. Using charge sensing, we show the ability to completely empty the dot of holes and control the charge occupation in the few-hole regime. The device should allow for control of individual hole spins in single and double quantum dots in GaAs.
Two-dimensional electron gas (2DEG) in interfaces and surfaces based on perovskite SrTiO$_3$ (STO) has exhibited various interesting phenomena and is used to develop oxide electronics. Recently, KTaO$_3$ (KTO) shows great potential and is believed to host more exciting effects and phenomena toward novel devices. Here, through first-principles investigation and analysis, we find two types of coexisting 2DEG and 2D hole gas (2DHG) highly confined at the interfaces in undoped STO/KTO/BaTiO$_3$ heterostructures, when the KTO thickness $m$ reaches a crititcal value. The two interfaces are made by (…
Spin-selective tunneling of holes in SiGe nanocrystals contacted by normal-metal leads is reported. The spin selectivity arises from an interplay of the orbital effect of the magnetic field with the strong spin-orbit interaction present in the valence band of the semiconductor. We demonstrate both experimentally and theoretically that spin-selective tunneling in semiconductor nanostructures can be achieved without the use of ferromagnetic contacts. The reported effect, which relies on mixing the light and heavy holes, should be observable in a broad class of quantum-dot systems formed in semic…
Spin qubits in silicon quantum dots offer a promising platform for a quantum computer as they have a long coherence time and scalability. The charge sensing technique plays an essential role in reading out the spin qubit as well as tuning the device parameters and therefore its performance in terms of measurement bandwidth and sensitivity is an important factor in spin qubit experiments. Here we demonstrate fast and sensitive charge sensing by a radio-frequency reflectometry of an undoped, accumulation-mode Si/SiGe double quantum dot. We show that the large parasitic capacitance in typical acc…
Recently, lithographic quantum dots in strained-Ge/SiGe have become a promising candidate for quantum computation, with a remarkably quick progression from demonstration of a quantum dot to qubit logic demonstrations. Here we present a measurement of the out-of-plane $g$-factor for single-hole quantum dots in this material. As this is a single-hole measurement, this is the first experimental result that avoids the strong orbital effects present in the out-of-plane configuration. In addition to verifying the expected $g$-factor anisotropy between in-plane and out-of-plane magnetic ($B$)-fields,…
We report on a magnetotransport study in a high-mobility 2D hole gas hosted in a pure Ge/SiGe quantum well subject to dc electric fields and high frequency microwave radiation. We find that under applied dc bias the differential resistivity exhibits a pronounced maximum at a magnetic field which increases linearly with the applied current. We associate this maximum with the fundamental peak of Hall field-induced resistance oscillations (HIRO) which are known to occur in 2D electron gases in GaAs/AlGaAs systems. After taking into account the Dingle factor correction, we find that the position o…
Disorder signatures emerging at millikelvin temperatures in Si/SiGe field-effect stacks
JARA-FIT Institute for Quantum Information, Forschungszentrum Jülich GmbH and RWTH Aachen University（约利希研究中心与亚琛工业大学）；IHP - Leibniz Institute for High Performance Microelectronics（莱布尼茨高性能微电子研究所）；Dipartimento di Scienze, Università Roma Tre（罗马第三大学科学系）；Fakultät für Physik, Universität Regensburg（雷根斯堡大学物理学院）
We investigate transport and Coulomb drag properties of semiconductor-based electron-hole bilayer systems. Our calculations are motivated by recent experiments in undoped electron-hole bilayer structures based on GaAs-AlGaAs gated double quantum well systems. Our results indicate that the background charged impurity scattering is the most dominant resistive scattering mechanism in the high-mobility bilyers. We also find that the drag transresistivity is significantly enhanced when the electron-hole layer separation is small due to the exchange induced renormalization of the single layer compre…
The epitaxial growth of germanium on silicon leads to the self-assembly of SiGe nanocrystals via a process that allows the size, composition and position of the nanocrystals to be controlled. This level of control, combined with an inherent compatibility with silicon technology, could prove useful in nanoelectronic applications. Here we report the confinement of holes in quantum-dot devices made by directly contacting individual SiGe nanocrystals with aluminium electrodes, and the production of hybrid superconductorsemiconductor devices, such as resonant supercurrent transistors, when the dot …
We present the fabrication details of completely undoped electron-hole bilayer devices in a GaAs/AlGaAs double quantum well heterostructure with a 30 nm barrier. These devices have independently tunable densities of the two-dimensional electron gas and two-dimensional hole gas. We report four-terminal transport measurements of the independently contacted electron and hole layers with balanced densities from $1.2 \times 10^{11}$cm$^{-2}$ down to $4 \times 10^{10}$ cm$^{-2}$ at $T = 300 mK$. The mobilities can exceed $1 \times 10^{6}$ cm$^{2}$ V$^{-1}$ s$^{-1}$ for electrons and $4 \times 10^{5}…
We examine the magnetic field driven insulator-quantum Hall-insulator transitions of the two dimensional hole gas in a Ge/SiGe quantum well. We observe direct transitions between low and high magnetic field insulators and the $ν=1$ quantum Hall state. With increasing magnetic field, the transitions from insulating to quantum Hall and quantum Hall to insulating are very similar with respect to their transport properties. We address the temperature dependence around the transitions and show that the characteristic energy scale for the high field transition is larger.
We report on a strong transport anisotropy in a 2D hole gas in a Ge/SiGe quantum well, which emerges only when both perpendicular and in-plane magnetic fields are present. The ratio of resistances, measured along and perpendicular to the in-plane field, can exceed $3\times 10^4$. The anisotropy occurs in a wide range of filling factors where it is determined {\em primarily} by the tilt angle. The lack of significant anisotropy without an in-plane field, easy tunability, and persistence to higher temperatures and filling factors set this anisotropy apart from nematic phases in GaAs/AlGaAs.
Disentangling orbital and confinement contributions to $g$-factor in Ge/SiGe hole quantum dots
IBM Research Europe – Zürich（IBM欧洲苏黎世研究中心）；IBM Quantum, T. J. Watson Research Center（IBM量子T.J.沃森研究中心）；Solid State Physics Laboratory, ETH Zürich（苏黎世联邦理工学院固体物理实验室）
We have fabricated AlGaAs/GaAs heterostructure devices in which the conduction channel can be populated with either electrons or holes simply by changing the polarity of a gate bias. The heterostructures are entirely undoped, and carriers are instead induced electrostatically. We use these devices to perform a direct comparison of the scattering mechanisms of two-dimensional (2D) electrons ($μ_\textrm{peak}=4\times10^6\textrm{cm}^2/\textrm{Vs}$) and holes ($μ_\textrm{peak}=0.8\times10^6\textrm{cm}^2/\textrm{Vs}$) in the same conduction channel with nominally identical disorder potentials. We f…
The layer interdependence of transport in an undoped electron-hole bilayer (uEHBL) device was studied as a function of carrier density, interlayer electric field, and temperature. The uEHBL device consisted of a density tunable, independently contacted two-dimensional electron gas (2DEG) and two-dimensional hole gas (2DHG) induced via field effect in distinct GaAs quantum wells separated by a 30 nm Al$_{0.9}$Ga$_{0.1}$As barrier. Transport measurements were made simultaneously on each layer using the van der Pauw method. An increase in 2DHG mobility with increasing 2DEG density was observed, w…
The effective g-factor of 2D holes in modulation doped \mbox{p-SiGe/Ge/SiGe} structures was studied. The AC conductivity of samples with hole densities from $3.9 \times 10^{11}$~to $6.2 \times 10^{11}~\text{cm}^{-2}$ was measured in perpendicular magnetic fields up to $8~\text{T}$ using a contactless acoustic method. From the analysis of the temperature dependence of conductivity oscillations, the $\mathrm{g}_{\perp}$-factor of each sample was determined. The $\mathrm{g}_{\perp}$-factor was found to be decreasing approximately linearly with hole density. This effect is attributed to non-parabo…
We fabricate an undoped Ge quantum well under 30 nm Ge0.8Si0.2 shallow barrier with reverse grading technology. The under barrier is deposited by Ge0.8Si0.2 followed by Ge0.9Si0.1 so that the variation of Ge content forms a sharp interface which can suppress the threading dislocation density penetrating into undoped Ge quantum well. And the Ge0.8Si0.2 barrier introduces enough in-plane parallel strain -0.41% in the Ge quantum well. The heterostructure field-effect transistors with a shallow buried channel get a high two-dimensional hole gas (2DHG) mobility over 2E6 cm2/Vs at a low percolation …
The pumping intensity (I) dependence of the photoluminescence (PL) spectra of perfectly laterally two-dimensionally ordered SiGe quantum dots on Si(001) substrates was studied. The PL results from recombinations of holes localized in the SiGe quantum dots and electrons localized due to the strain field in the surrounding Si matrix. The analysis of the spectra revealed several distinct bands, attributed to phonon-assisted recombination and no-phonon recombination of the excitonic ground state and of the excited excitonic states, which all exhibit a linear I dependence of the PL intensity. At ap…
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…
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…
We report experimental evidence of ballistic hole transport in one-dimensional quantum wires gate-defined in a strained SiGe/Ge/SiGe quantum well. At zero magnetic field, we observe conductance plateaus at integer multiples of 2e^2/h. At finite magnetic field, the splitting of these plateaus by Zeeman effect reveals largely anisotropic g-factors, with absolute values below 1 in the quantum-well plane, and exceeding 10 out of plane. This g-factor anisotropy is consistent with a heavy-hole character of the propagating valence-band states, in line with a predominant confinement in the growth dire…
High-conductivity undoped GaN/AlN 2D hole gases (2DHGs), the p-type dual of the AlGaN/GaN 2D electron gases (2DEGs), have offered valuable insights into hole transport in GaN and enabled the first GaN GHz RF p-channel FETs. They are an important step towards high-speed and high-power complementary electronics with wide-bandgap semiconductors. These technologically and scientifically relevant 2D hole gases are perceived to be not as robust as the 2DEGs because structurally similar heterostructures exhibit wide variations of the hole density over $Δp_s >$ 7 x 10$^{13}$ cm$^{-2}$, and low mobilit…
