Ge Hut Research Articles

Ultrafast and Electrically Tunable Rabi Frequency in a Germanium Hut Wire Hole Spin Qubit

Hole spin qubits based on germanium (Ge) have strong tunable spin-orbit interaction (SOI) and ultrafast qubit operation speed. Here we report that the Rabi frequency (fRabi) of a hole spin qubit in a Ge hut wire (HW) double quantum dot (DQD) is electrically tuned through the detuning energy (ϵ) and middle gate voltage (VM). fRabi gradually decreases with increasing ϵ; on the contrary, fRabi is positively correlated with VM. We attribute our results to the change of electric field on SOI and the contribution of the excited state in quantum dots to fRabi. We further demonstrate an ultrafast fRabi exceeding 1.2 GHz, which indicates the strong SOI in our device. The discovery of an ultrafast and electrically tunable fRabi in a hole spin qubit has potential applications in semiconductor quantum computing.

Strain-induced ordered Ge(Si) hut wires on patterned Si (001) substrates.

Ge/Si nanowires are predicted to be a promising platform for spin and even topological qubits. While for large-scale integration of these devices, nanowires with fully controlled positions and arrangements are a prerequisite. Here, we have reported ordered Ge hut wires by multilayer heteroepitaxy on patterned Si (001) substrates. Self-assembled GeSi hut wire arrays are orderly grown inside patterned trenches with post growth surface flatness. Such embedded GeSi wires induce tensile strain on the Si surface, which results in preferential nucleation of Ge nanostructures. Ordered Ge nano-dashes, disconnected wires and continuous wires are obtained correspondingly by tuning the growth conditions. These site-controlled Ge nanowires on a flattened surface lead to the ease of fabrication and large-scale integration of nanowire quantum devices.

Magnetic transport measurements of spin–orbit and hyperfine interactions in a Ge hut wire double quantum dot

Ge quantum dots are emerging as an attractive platform to realize high-fidelity qubits because of their strong spin–orbit interaction (SOI) and weak hyperfine interaction (HFI). Here, we measure and analyze the transport spectra on a highly tunable double quantum dot (DQD) defined in Ge hut wires with an external out-of-plane magnetic field. At a high magnetic field, the SOI induced spin-flip tunneling lifts the Pauli spin blockade and maps out the energy spectrum of the DQD. At a low magnetic field, the HFI mixes the (1, 1) states and leads to an enhanced leakage current, which is affected by the inter-dot tunnel coupling.

Anisotropic g-Factor and Spin-Orbit Field in a Germanium Hut Wire Double Quantum Dot.

Holes in nanowires have drawn significant attention in recent years because of the strong spin-orbit interaction, which plays an important role in constructing Majorana zero modes and manipulating spin-orbit qubits. Here, from the strongly anisotropic leakage current in the spin blockade regime for a double dot, we extract the full g-tensor and find that the spin-orbit field is in plane with an azimuthal angle of 59° to the axis of the nanowire. The direction of the spin-orbit field indicates a strong spin-orbit interaction along the nanowire, which may have originated from the interface inversion asymmetry in Ge hut wires. We also demonstrate two different spin relaxation mechanisms for the holes in the Ge hut wire double dot: spin-flip co-tunneling to the leads, and spin-orbit interaction within the double dot. These results help establish feasibility of a Ge-based quantum processor.

Dipole coupling of a hole double quantum dot in germanium hut wire to a microwave resonator

The germanium (Ge) hut wire system has strong spin–orbit coupling, a long coherence time due to a very large heavy-light hole splitting, and the advantage of site-controlled large-scale hut wire positioning. These properties make the Ge hut wire a promising candidate for the realization of strong coupling of spin to superconducting resonators and scalability for multiple qubit coupling. We have coupled a reflection line resonator to a hole double quantum dot (DQD) formed in Ge hut wire. The amplitude and phase responses of the microwave resonator revealed that the charge stability diagrams of the DQD are in good agreement with those obtained from transport measurements. The DQD interdot tunneling rate is shown to be tunable from 6.2 GHz to 8.5 GHz, which demonstrates the ability to adjust the frequency detuning between the qubit and the resonator. Furthermore, we achieved a hole–resonator coupling strength of up to 15 MHz, with a charge qubit decoherence rate of 0.28 GHz. Meanwhile the hole spin–resonator coupling rate was estimated to be 3 MHz. These results suggest that holes of a DQD in a Ge hut wire are dipole coupled to microwave photons, potentially enabling tunable hole spin–photon interactions in Ge with an inherent spin–orbit coupling.

Zero Field Splitting of Heavy-Hole States in Quantum Dots.

Using inelastic cotunneling spectroscopy we observe a zero field splitting within the spin triplet manifold of Ge hut wire quantum dots. The states with spin ±1 in the confinement direction are energetically favored by up to 55 μeV compared to the spin 0 triplet state because of the strong spin–orbit coupling. The reported effect should be observable in a broad class of strongly confined hole quantum-dot systems and might need to be considered when operating hole spin qubits.

Hole spin in tunable Ge hut wire double quantum dot

Holes in germanium (Ge) exhibit strong spin–orbit interaction, which can be exploited for fast and all-electrical manipulation of spin states. Here, we report transport experiments in a tunable Ge hut wire hole double quantum dot. We observe the signatures of Pauli spin blockade (PSB) with a large singlet-triplet energy splitting of ∼1.1 meV and extract the g factor. By analyzing the PSB leakage current, we obtain a spin–orbit length of ∼40–100 nm. Furthermore, we demonstrate the electric dipole spin resonance. These results lay a solid foundation for implementing high quality tunable hole spin–orbit qubits.

The formation of intermediate layers in covered Ge/Si heterostructures with low-temperature quantum dots: a study using high-resolution transmission electron microscopy and Raman spectroscopy

The method of software analysis of high-resolution TEM images using the peak pairs algorithm [Galindo P L et al 2007 Ultramicroscopy 107 1186–93] in combination with Raman spectroscopy was employed to study lattice deformations in Ge/Si(001) structures with low-temperature Ge quantum dots. It was found that the stresses do not spread in a thick Si layer above quantum dots, but completely relax via the formation of a thin boundary layer of mixed composition. However, intermixing of Ge and Si is absent beneath the Ge layer in samples with a Ge coverage of 10 Å. Besides intermixing was not observed at all, both beneath and above the Ge layer, in samples with a Ge coverage of 6 Å or less. This may be due to the predominance of Ge diffusion into the Si matrix from the {105} facets of Ge huts, not from the Ge wetting layer, at low temperatures of the Ge/Si structure deposition. The critical thickness of Si coverage at which the intense stress-induced diffusion takes place is determined to lie in the range from 5 to 8 nm.

Measuring the complex admittance and tunneling rate of a germanium hut wire hole quantum dot

We investigate the microwave reflectometry of an on-chip reflection line cavity coupled to a Ge hut wire hole quantum dot. The amplitude and phase responses of the cavity can be used to measure the complex admittance and evaluate the tunneling rate of the quantum dot, even in the region where transport signal through the quantum dot is too small to be measured by conventional direct transport means. The experimental observations are found to be in good agreement with a theoretical model of the hybrid system based on cavity frequency shift and linewidth shift. Our experimental results take the first step towards fast and sensitive readout of charge and spin states in Ge hut wire hole quantum dot.

Ballistic Hole Emission Spectroscopy of Self-Assembled GeSi/Si(001) Nanoislands

Ballistic hole emission microscopy/spectroscopy has been applied to study the electronic structure of the hole states in the self-assembled GeSi/Si(001) nanoislands. The ballistic hole emission microscopic images demonstrated the spots of increased collector current related to the ballistic electron tunnelling via the confined valence band states in the GeSi/Si(001) nanoislands. In the ballistic hole emission spectra of the Ge hut clusters the stepwise features attributed to the quantum confined hole states have been observed. The results of present study demonstrate the capabilities of the ballistic hole emission microscopy/spectroscopy in the characterization of the electronic structures of the valence band states in the GeSi/Si nanostructures.

Coupling a Germanium Hut Wire Hole Quantum Dot to a Superconducting Microwave Resonator.

Realizing a strong coupling between spin and resonator is an important issue for scalable quantum computation in semiconductor systems. Benefiting from the advantages of a strong spin-orbit coupling strength and long coherence time, the Ge hut wire, which is proposed to be site-controlled grown for scalability, is considered to be a promising candidate to achieve this goal. Here we present a hybrid architecture in which an on-chip superconducting microwave resonator is coupled to the holes in a Ge quantum dot. The charge stability diagram can be obtained from the amplitude and phase responses of the resonator independently from the DC transport measurement. Furthermore, we estimate the hole-resonator coupling rate of gc/2π = 148 MHz in the single quantum dot-resonator system and estimate the spin-resonator coupling rate gs/2π to be in the range 2-4 MHz. We anticipate that strong coupling between hole spins and microwave photons in a Ge hut wire is feasible with optimized schemes in the future.

Ballistic hole emission spectroscopy of self-assembled GeSi/Si(001) nanoislands

AbstractBallistic hole emission microscopy/spectroscopy has been applied to study the electronic structure of the hole states in the self-assembled GeSi/Si(001) nanoislands. The ballistic hole emission microscopic images demonstrated the spots of increased collector current related to the ballistic electron tunnelling via the confined valence band states in the GeSi/Si(001) nanoislands. In the ballistic hole emission spectra of the Ge hut clusters the stepwise features attributed to the quantum confined hole states have been observed. The results of present study demonstrate the capabilities of the ballistic hole emission microscopy/spectroscopy in the characterization of the electronic structures of the valence band states in the GeSi/Si nanostructures.

Efficient Calculation of Electronic Structure Using O(N) Density Functional Theory.

We propose an efficient way to calculate the electronic structure of large systems by combining a large-scale first-principles density functional theory code, Conquest, and an efficient interior eigenproblem solver, the Sakurai-Sugiura method. The electronic Hamiltonian and charge density of large systems are obtained by Conquest, and the eigenstates of the Hamiltonians are then obtained by the Sakurai-Sugiura method. Applications to a hydrated DNA system and adsorbed P2 molecules and Ge hut clusters on large Si substrates demonstrate the applicability of this combination on systems with 10,000+ atoms with high accuracy and efficiency.

Heavy-Hole States in Germanium Hut Wires.

Hole spins have gained considerable interest in the past few years due to their potential for fast electrically controlled qubits. Here, we study holes confined in Ge hut wires, a so-far unexplored type of nanostructure. Low-temperature magnetotransport measurements reveal a large anisotropy between the in-plane and out-of-plane g-factors of up to 18. Numerical simulations verify that this large anisotropy originates from a confined wave function of heavy-hole character. A light-hole admixture of less than 1% is estimated for the states of lowest energy, leading to a surprisingly large reduction of the out-of-plane g-factors compared with those for pure heavy holes. Given this tiny light-hole contribution, the spin lifetimes are expected to be very long, even in isotopically nonpurified samples.

Nanoscale thermal transport in self-organized epitaxial Ge nanostructures on Si(001)

The thermal transport properties of self-organized Ge nanostructures on Si were studied by means of ultrafast surface sensitive time-resolved electron diffraction. The thermal boundary resistance was determined from the temperature response of the Ge nanostructures upon impulsive heating by fs-laser pulses. The transient temperature was determined through the Debye–Waller effect. Epitaxial growth of Ge hut and dome clusters was achieved by in-situ deposition of 8 monolayers of Ge on Si(001) at 550 °C under ultra-high vacuum conditions. Time-resolved spot profile analysis of different orders of diffraction spots was used to distinguish between the thermal response of hut and dome clusters. Dome clusters of 6 nm height and 50 nm width cool with a time constant of which agrees well with numerical simulations calculated in the framework of the diffuse mismatch model. The much smaller hut clusters with a height of 2.3 nm and width of 23 nm exhibit a cooling time of , which is a factor of 2 slower than predicted by theory.

Nanoscale heat transport from Ge hut, dome, and relaxed clusters on Si(001) measured by ultrafast electron diffraction

The thermal transport properties of crystalline nanostructures on Si were studied by ultra-fast surface sensitive time-resolved electron diffraction. Self-organized growth of epitaxial Ge hut, dome, and relaxed clusters was achieved by in-situ deposition of 8 monolayers of Ge on Si(001) at 550 °C under UHV conditions. The thermal response of the three different cluster types subsequent to impulsive heating by fs laser pulses was determined through the Debye-Waller effect. Time resolved spot profile analysis and life-time mapping was employed to distinguish between the thermal response of the different cluster types. While dome clusters are cooling with a time constant of τ = 150 ps, which agrees well with numerical simulations, the smaller hut clusters with a height of 2.3 nm exhibit a cooling time constant of τ = 50 ps, which is a factor of 1.4 slower than expected.

Ge/Si Heterostructures with Dense Chains of Stacked Quantum Dots

An overview of new results on growth and characterization of Ge/Si(001) heterostructures with dense chains of stacked Ge quantum dots is reported. Ge hut nucleation and growth at low temperatures is discussed on the basis of results obtained by high resolution scanning tunneling microscopy and in-situ reflected high-energy electron diffraction. Atomic-level models of nucleating and growing huts are considered. Recent data of high resolution transmission electron microscopy are presented focusing on long chains of Ge quantum dots synthesised in silicon matrix by means of molecular beam epitaxy at low-temperature mode. Approaches to formation of three dimensional ordered arrays of Ge cluster and Ge quantum dot crystals are considered in special detail.

On atomic structure of Ge huts growing on the Ge/Si(001) wetting layer

Structural models of growing Ge hut clusters—pyramids and wedges—are proposed on the basis of data of recent STM investigations of nucleation and growth of Ge huts on the Si(001) surface in the process of molecular beam epitaxy. It is shown that extension of a hut base along ⟨110⟩ directions goes non-uniformly during the cluster growth regardless of its shape. Growing pyramids, starting from the second monolayer, pass through cyclic formation of slightly asymmetrical and symmetrical clusters, with symmetrical ones appearing after addition of every fourth monolayer. We suppose that pyramids of symmetrical configurations composed by 2, 6, 10, etc., monolayers over the wetting layer are more stable than asymmetrical ones. This might explain less stability of pyramids in comparison with wedges in dense arrays forming at low temperatures of Ge deposition. Possible nucleation processes of pyramids and wedges on wetting layer patches from identical embryos composed by 8 dimers through formation of 1 monolayer high 16-dimer nuclei different only in their symmetry is discussed. Schematics of these processes are presented. It is concluded from precise STM measurements that top layers of wetting layer patches are relaxed when huts nucleate on them.

Ge/Si(001) heterostructures with dense arrays of Ge quantum dots: morphology, defects, photo-emf spectra and terahertz conductivity

Issues of Ge hut cluster array formation and growth at low temperatures on the Ge/Si(001) wetting layer are discussed on the basis of explorations performed by high resolution STM and in-situ RHEED. Dynamics of the RHEED patterns in the process of Ge hut array formation is investigated at low and high temperatures of Ge deposition. Different dynamics of RHEED patterns during the deposition of Ge atoms in different growth modes is observed, which reflects the difference in adatom mobility and their ‘condensation’ fluxes from Ge 2D gas on the surface for different modes, which in turn control the nucleation rates and densities of Ge clusters. Data of HRTEM studies of multilayer Ge/Si heterostructures are presented with the focus on low-temperature formation of perfect films.Heteroepitaxial Si p–i–n-diodes with multilayer stacks of Ge/Si(001) quantum dot dense arrays built in intrinsic domains have been investigated and found to exhibit the photo-emf in a wide spectral range from 0.8 to 5 μm. An effect of wide-band irradiation by infrared light on the photo-emf spectra has been observed. Photo-emf in different spectral ranges has been found to be differently affected by the wide-band irradiation. A significant increase in photo-emf is observed in the fundamental absorption range under the wide-band irradiation. The observed phenomena are explained in terms of positive and neutral charge states of the quantum dot layers and the Coulomb potential of the quantum dot ensemble. A new design of quantum dot infrared photodetectors is proposed.By using a coherent source spectrometer, first measurements of terahertz dynamical conductivity (absorptivity) spectra of Ge/Si(001) heterostructures were performed at frequencies ranged from 0.3 to 1.2 THz in the temperature interval from 300 to 5 K. The effective dynamical conductivity of the heterostructures with Ge quantum dots has been discovered to be significantly higher than that of the structure with the same amount of bulk germanium (not organized in an array of quantum dots). The excess conductivity is not observed in the structures with the Ge coverage less than 8 Å. When a Ge/Si(001) sample is cooled down the conductivity of the heterostructure decreases.

Ge quantum dot arrays grown by ultrahigh vacuum molecular-beam epitaxy on the Si(001) surface: nucleation, morphology, and CMOS compatibility

Issues of morphology, nucleation, and growth of Ge cluster arrays deposited by ultrahigh vacuum molecular beam epitaxy on the Si(001) surface are considered. Difference in nucleation of quantum dots during Ge deposition at low (≲600°C) and high (≳600°C) temperatures is studied by high resolution scanning tunneling microscopy. The atomic models of growth of both species of Ge huts--pyramids and wedges-- are proposed. The growth cycle of Ge QD arrays at low temperatures is explored. A problem of lowering of the array formation temperature is discussed with the focus on CMOS compatibility of the entire process; a special attention is paid upon approaches to reduction of treatment temperature during the Si(001) surface pre-growth cleaning, which is at once a key and the highest-temperature phase of the Ge/Si(001) quantum dot dense array formation process. The temperature of the Si clean surface preparation, the final high-temperature step of which is, as a rule, carried out directly in the MBE chamber just before the structure deposition, determines the compatibility of formation process of Ge-QD-array based devices with the CMOS manufacturing cycle. Silicon surface hydrogenation at the final stage of its wet chemical etching during the preliminary cleaning is proposed as a possible way of efficient reduction of the Si wafer pre-growth annealing temperature.