Strained Silicon Quantum Research Articles

Low Disorder and High Mobility 2DEG in Si/SiGe Fabricated in 200 mm BiCMOS Pilot line

Spin qubits based on quantum dots built on Si/SiGe heterostructures are a leading contender for achieving large-scale quantum computation. The quality of quantum dots fabricated on these heterostructures is directly connected to the quality of the 2D electron gas (2DEG) confined in the strained Silicon quantum well. The properties of such 2DEG can be readily assessed using Hall bar-shaped field-effect transistors (HB-FETs) and magneto-transport measurements, enabling a faster feedback loop for heterostructure optimization process. In this work, we present our recent progress in enabling silicon-based quantum computation by demonstrating fundamental components for 2DEG characterization, all developed in IHP's 200 mm BiCMOS pilot line. We demonstrate fully functional HB-FETs on Si/SiGe heterostructures grown on 200 mm silicon wafers, showcasing state-of-the-art 2DEG with maximum carrier mobility exceeding 300,000 cm²/Vs and a percolation threshold of 6.3×1010 cm⁻². These results will help advance spin qubit research based on Si/SiGe heterostructures.

High-resolution x-ray reflection Fourier analysis of metamorphic Si/SiGe quantum wells

Graded buffer metamorphic epitaxial heterostructures are extraordinarily difficult to analyze using x-ray diffraction because of large signal contributions from the buffer. As an alternative, Fourier signal processing is applied to x-ray reflectivity data such that layer thickness and reflectivity strength are readily extracted. This analysis is applied to two strained silicon quantum wells grown inside relaxed silicon germanium barriers. Analysis of the x-ray reflectivity data directly determines that the quantum wells are 8.5 and 8.7 nm spaced by a 22.0-nm thick barrier. These values agree with those extracted from transmission electron microscopy to better than 0.5 nm.

Optical characterization of a strained silicon quantum well on SiGe on insulator

An 8nm thick strained silicon layer embedded in relaxed Si0.8Ge0.2 has been grown on SiGe on insulator substrate in order to reduce the optical response of dislocations present in the SiGe virtual substrate. Photoreflectance measurement shows bandgap shrinkage at Γ point of 0.19eV which corresponds to a 0.94% strain value close to the one measured in Raman spectroscopy. The luminescence arising only from the strained Si quantum well in high injection conditions reveals clearly two optical transitions observed at 0.959 and 1.016eV.

Valley splitting in strained silicon quantum wells modeled with 2° miscuts, step disorder, and alloy disorder

Valley splitting (VS) in strained SiGe∕Si∕SiGe quantum wells grown on (001) and 2° miscut substrates is computed in a magnetic field. Calculations of flat structures significantly overestimate, while calculations of perfectly ordered structures underestimate experimentally observed VS. Step disorder and confinement alloy disorder raise the VS to the experimentally observed levels. Atomistic alloy disorder is identified as the critical physics, which cannot be modeled with analytical effective mass theory. NEMO-3D is used to simulate up to 106 atoms, where strain is computed in the valence-force field and electronic structure in the sp3d5s* model.

Zero Valley Splitting at Zero Magnetic Field for Strained Si/SiGe Quantum Wells

AbstractThe electronic structure for a strained silicon quantum well grown on a tilted SiGe substrate is calculated using an empirical tight-binding method. For a zero substrate tilt angle the two lowest minima of the conduction band define a non-zero valley splitting at the center of the Brillouin zone. A finite tilt angle for the substrate results in displacing the two lowest conduction band minima to finite k0 and -k0 in the Brillouin zone with equal energy. The vanishing of the valley splitting for quantum wells grown on tilted substrates is found to be a direct consequence of the periodicity of the steps at the interfaces between the quantum well and the buffer materials.

Magnetic-field dependence of valley splitting in Si quantum wells grown on tilted SiGe substrates

The valley splitting of the first few Landau levels is calculated as a function of the magnetic field for electrons confined in a strained silicon quantum well grown on a tilted SiGe substrate, using a parameterized tight-binding method. For a zero substrate tilt angle, the valley splitting slightly decreases with increasing magnetic field. In contrast, the valley splitting for a finite substrate tilt angle exhibits a strong and non-monotonous dependence on the magnetic field strength. The valley splitting of the first Landau level shows an exponential increase followed by a slow saturation as the magnetic field strength increases. The valley splitting of the second and third Landau levels shows an oscillatory behavior. The non-monotonous dependence is explained by the phase variation of the Landau level wave function along the washboard-like interface between the tilted quantum well and the buffer material. The phase variation is the direct consequence of the misorientation between the crystal axis and the confinement direction of the quantum well. This result suggests that the magnitude of the valley splitting can be tuned by controlling the Landau-level filling factor through the magnetic field and the doping concentration.

Simulation of Si:P spin-based quantum computer architecture

We present a systematic and realistic simulation for single and double phosphorous donors in a silicon-based quantum computer design. A two-valley equation is developed to describe the ground state of phosphorous donors in strained silicon quantum well (QW), with the central cell effect treated by a model impurity potential. We find that the increase of quantum well confinement leads to shrinking charge distribution in all 3 dimensions. Using an unrestricted Hartree-Fock method with Generalized Valence Bond (GVB) single-particle wave functions, we are able to solve the two-electron Sch${\ddot o}$dinger equation with quantum well confinement and realistic gate potentials. The effects of QW width, gate voltages, donor separation, and donor position are calculated and analyzed. The gate tunability and gate fidelity are defined and evaluated, for a typical QC design. Estimates are obtained for the duration of $\sqrt{SWAP}$ gate operation and the required accuracy in voltage control. A strong exchange oscillation is observed as both donors are shifted along [001] axis but with their separation unchanged. Applying a gate potential tends to suppress the oscillation. The exchange oscillation as a function of donor position along [100] axis is found to be completely suppressed as the donor separation is decreased. The simulation presented in this paper is of importance to the practical design of an exchange-based silicon quantum computer.

Valley splitting in V-shaped quantum wells

The valley splitting (energy difference between the states of the lowest doublet) in strained silicon quantum wells with a V-shaped potential is calculated variationally using a two-band tight-binding model. The approximation is valid for a moderately long (approximately 5.5–13.5nm) quantum well with a V-shaped potential which can be produced by a realistic delta-doping on the order of nd≈1012cm−2. The splitting versus applied field (steepness of the V-shaped potential) curves show interesting behavior: a single minimum and for some doublets, a parity reversal as the field is increased. These characteristics are explained through an analysis of the variational wave function and energy functional.

Photoluminescence of a tensilely strained silicon quantum well on a relaxed SiGe buffer layer

We have investigated the photoluminescence of tensilely strained silicon layers grown on relaxed SiGe buffer layers. At low excitation densities, the photoluminescence is dominated by the radiative recombinations associated with the dislocations in the buffer layer and the band-edge luminescence of the relaxed SiGe layers. We show that the photoluminescence of a strained silicon quantum well capped by a relaxed SiGe layer can be observed at high excitation densities. The resonance energy of this photoluminescence, observed around 960meV for the phonon-assisted transition, is in satisfying agreement with the calculated value of the bandgap of the type II strained heterostructure.

Valley splitting in strained silicon quantum wells

A theory based on localized-orbital approaches is developed to describe the valley splitting observed in silicon quantum wells. The theory is appropriate in the limit of low electron density and relevant for quantum computing architectures. The valley splitting is computed for realistic devices using the quantitative nanoelectronic modeling tool NEMO. A simple, analytically solvable tight-binding model reproduces the behavior of the splitting in the NEMO results and yields much physical insight. The splitting is in general nonzero even in the absence of electric field in contrast to previous works. The splitting in a square well oscillates as a function of S, the number of layers in the quantum well, with a period that is determined by the location of the valley minimum in the Brillouin zone. The envelope of the splitting decays as S−3. The feasibility of observing such oscillations experimentally in Si/SiGe heterostructures is discussed.

Germanium islands embedded in strained silicon quantum wells grown on patterned substrates

Germanium islands were embedded in strained silicon quantum wells in order to provide an improved electron confinement in vicinity of the islands. Growth was performed on relaxed SiGe layers. Patterned substrates were used, favouring lattice relaxation as well permitting the fabrication of small Ge islands at deposition temperatures above 500°C. Photoluminescence analysis reveals a strongly reduced dislocation related signal. The low temperature spectra are dominated by intense signals from the germanium islands. The origin of these signals were investigated by removing the islands by etching, analysing reference samples without a silicon quantum well, varying the germanium deposition and the growth temperature.

Cryogenic field effect transistors using strained silicon quantum wells in Si:SiGe heterostructures grown by APCVD

High mobility strained silicon quantum wells in modulation doped SiGe heterostructures, grown epitaxially on silicon substrates, offer exciting opportunities for devices compatible with silicon CMOS processing, having significantly improved performance over their single crystal silicon counterparts. We present results from a collaborative academic/industrial program to develop field effect transistors suitable for cryogenic circuit applications. This work reports on the fabrication and characterization of heterostructure material grown using atmospheric pressure CVD, low temperature characterization of the electronic properties of the material, FET device fabrication and FET performance at 0.3–4.2 K.

Quantum wires in strained silicon quantum wells on tilted substrates

Quantum wires have been fabricated in strained silicon heterostructures grown on 2∘tilted substrates. Magnetoresistance of both wires and Hall bars have been examined at 0.3 K for slow Shubnikov–de Haas (SdH) oscillations that would indicate the formation of minigaps in the band structure of off-axis electron transport. Structures were oriented both parallel and perpendicular to the step edges. The Hall bar structures exhibit no evidence of miniband formation at 0.3 K, and little anisotropy other than slightly reduced carrier density and mobility in the perpendicular Hall bar. The quantum wires are decidedly more modulated by low-frequency oscillations, and exhibit anisotropic behavior.

Characterization of strained silicon quantum wells and Si1-xGex heterostructures using Auger electron spectroscopy and spreading resistance profiles of bevelled structures

Critical fabrication parameters of modulation-doped Si/ SiGe heterostructures may be extensively and quickly characterized using a combination of spreading resistance profile measurements and scanning Auger electron spectroscopy on bevelled heterostructures. We have used this combined approach, with relatively accessible characterization tools, to determine the thickness, composition and doping concentrations in the supply, spacer, well, buffer and graded layers of the heterostructures. Depth profiles of the active layers and virtual substrate can be assessed in a straightforward manner, allowing for optimization of processing parameters and of the overall device structure.

Minigaps in strained silicon quantum wells on tilted substrates

The two-dimensional electron gas formed at the inverted surface of a tilted silicon substrate shows unusual magnetotransport properties due to the presence of a minigap in the density of states. For metal–oxide–semiconductor inversion layers the strong scattering at the interface limits the mobility to values μ<10–20 000 cm2/V s. To achieve mobilities approaching 105 cm2/V s we have used strained Si:SiGe quantum wells grown on substrates tilted away from the (001) normal by 0°, 2°, 4°, 6°, and 10°. Their transport properties have been measured in the temperature range of 20–500 mK. All the samples show strong Shubnikov–de Haas oscillations. For the 2° and 4° samples the envelope of the fast oscillations is modulated by a longer period oscillation at low magnetic fields. We attribute the slow oscillation in the 2° and 4° samples to the presence of a minigap. For the 6° and 10° samples the minigap is higher than the Fermi energy and is not expected to influence the transport properties.

Conduction bandstructure in strained silicon by spatially resolved electron energy loss spectroscopy

Silicon 2p core absorption near edge fine structure has been obtained by spatially resolved electron energy loss spectroscopy in strained silicon quantum wells. Extraction of the heterojunction band offset as a function of position in the wells appears to be possible with some caution. The band offset has been correlated with atomic composition using annular dark field, Z-contrast imaging. The results suggest that the poor electron mobility, found in one of the wells by standard electrical measurements, resulted from poor carrier screening in the presence of a heterojunction band offset which varied by as much as 50 meV from place to place within the well.

Strained Quantum Dots in Porous Silicon

ABSTRACTOn the basis of Raman, photoluminescence, and absorption studies of porous and nanoparticle silicon we propose that the strong luminescence in porous silicon results from strained silicon quantum dots. A silicon nanoparticle is a special Jahn-Teller system induced by extended electron states rather than localized state. Thus Raman scattering and photoluminescence in porous silicon are multi-phonon assisted free electronic transition processes, all observed anomalous properties of porous silicon can be clearly explained by using this strained quantum dot model.