Si Quantum Wells Research Articles

Polytypic quantum wells in Si and Ge: impact of 2D hexagonal inclusions on electronic band structure

This study reveals the impact of 2D hexagonal inclusions on Si and Ge, prompting their exploitation as light sources in Si photonics.

Origin of giant valley splitting in silicon quantum wells induced by superlattice barriers

Enhancing valley splitting in SiGe heterostructures is a crucial task for developing silicon spin qubits. Complex SiGe heterostructures, sharing a common feature of four-monolayer (4ML) Ge layer next to the silicon quantum well (QW), have been computationally designed to have giant valley splitting approaching 9 meV. However, none of them has been fabricated may due to their complexity. Here, we remarkably simplify the original designed complex SiGe heterostructures by laying out the Si QW directly on the Ge substrate followed by capping a (Ge4Si4)n superlattice(SL) barrier with a small sacrifice on VS as it is reduced from a maximum of 8.7 meV to 5.2 meV. Even the smallest number of periods (n = 1) will also give a sizable VS of 1.6 meV, which is large enough for developing stable spin qubits. We also develop an effective Hamiltonian model to reveal the underlying microscopic physics of enhanced valley splitting by (Ge4Si4)n SL barriers. We find that the presence of the SL barrier will reduce the VS instead of enhancing it. Only the (Ge4Si4)n SL barriers with an extremely strong coupling with Si QW valley states provide a remarkable enhancement in VS. These findings lay a solid theoretical foundation for the realization of sufficiently large VS for Si qubits.

Effect of Quantum Hall Edge Strips on Valley Splitting in Silicon Quantum Wells.

We determine the energy splitting of the conduction-band valleys in two-dimensional electrons confined to low-disorder Si quantum wells. We probe the valley splitting dependence on both perpendicular magnetic field B and Hall density by performing activation energy measurements in the quantum Hall regime over a large range of filling factors. The mobility gap of the valley-split levels increases linearly with B and is strikingly independent of Hall density. The data are consistent with a transport model in which valley splitting depends on the incremental changes in density eB/h across quantum Hall edge strips, rather than the bulk density. Based on these results, we estimate that the valley splitting increases with density at a rate of 116 μeV/10^{11} cm^{-2}, which is consistent with theoretical predictions for near-perfect quantum well top interfaces.

Спектр излучения и стабильность двух типов электронно-дырочной жидкости в мелких Si/Si-=SUB=-1-x-=/SUB=-Ge-=SUB=-x-=/SUB=-Si квантовых ямах

Abstract Based on calculations within the density functional theory and an analysis of low-temperature photoluminescence spectra, the structure of electron–hole liquid in shallow Si/Si_1 – _ x Ge_ x Si (100) quantum wells 5 nm wide with germanium content x = 3–5.5% is studied. It is shown that the energy of quasi-two-dimensional electron–hole liquid localized in quantum wells for this composition range as a function of carrier concentration exhibits two local minima. The position of the deeper (major) minimum depends on the quantum well design and controls properties of quasi-two-dimensional electron–hole liquid at low temperatures. For the series of Si/Si_1 – _ x Ge_ x Si quantum wells, modification of properties of electron–hole liquid was experimentally shown, which can be interpreted as a change of the major minimum due to an increases in the germanium concentration in the Si_1 – _ x Ge_ x layer. The effect of the multicomponent composition (electrons, light and heavy holes) of the electron–hole liquid on low-temperature photoluminescence spectra of Si/Si_1 ‒ _ x Ge_ x Si quantum wells is discussed.

Multijunction solar cells concept based on GaP/Si nanostructures

Abstract The lattice-matched GaP/Si superlattice is proposed to be used as an active material for top junction, which is grown on n–GaP/p-Si heterojunction bottom sub cell. Computer simulations demonstrate that GaP/Si structures with 1-2 nm Si quantum wells allow one to obtain a material with an effective band gap of 1.4–1.6 eV. GaP/Si nanostructures were grown at 380 °C by plasma deposition using PE-ALD and PECVD for GaP and Si layers growth, respectively. Structural, optical and electrical properties of GaP/Si nanostructures grown on Si and GaP wafers are reported and discussed in terms of photovoltaic application.

The critical role of substrate disorder in valley splitting in Si quantum wells

Atomic-scale disorder at the top interface of a Si quantum well is known to suppress valley splitting. Such disorder may be inherited from the underlying substrate and relaxed buffer growth, but can also arise at the top quantum well interface due to the random SiGe alloy. Here, we perform activation energy (transport) measurements in the quantum Hall regime to determine the source of the disorder affecting the valley splitting. We consider three Si/SiGe heterostructures with nominally identical substrates but different barriers at the top of the quantum well, including two samples with pure-Ge interfaces. For all three samples, we observe a surprisingly strong and universal dependence of the valley splitting on the electron density (Ev ∼ n2.7) over the entire experimental range (Ev = 30–200 μeV). We interpret these results via tight binding theory, arguing that the underlying valley physics is determined mainly by disorder arising from the substrate and relaxed buffer growth.

Valence-band offsets in strained SiGeSn/Si layers with different tin contents

Admittance spectroscopy is used to study hole states in Si0.7–y Ge0.3Sn y /Si quantum wells in the tin content range y = 0.04–0.1. It is found that the hole binding energy increases with tin content. The hole size-quantization energies in structures containing a pseudomorphic Si0.7–y Ge0.3Sn y layer in the Si matrix are determined using the 6-band kp method. The valence-band offset at the Si0.7–y Ge0.3Sn y heterointerface is determined by combining the numerical calculation results and experimental data. It is found that the dependence of the experimental values of the valence-band offsets between pseudomorphic Si0.7–y Ge0.3Sn y layers and Si on the tin content is described by the expression ΔE V exp = (0.21 ± 0.01) + (3.35 ± 7.8 × 10–4)y eV.

Strong photoluminescence from ultrathin silicon (110) quantum wells at room temperature

Strong room-temperature photoluminescence (PL) from SiO2/Si(110)/SiO2 quantum wells (QWs) is observed, for the first time. The PL intensity increases with the decrease of the Si(110) well thickness. Furthermore, when the upper SiO2 layer is removed, no PL peaks could be observed. But the luminescence is recovered when the samples were exposed to air for several months with the re-formation of Si–SiOx interface, and slightly dependent of temperature. These results indicate that both of the quantum confinement effect and the interface effect play an important role in the luminescence properties of Si(110) QWs.

Surface-oxide stress induced band-structure modulation in two-dimensional Si layers

We experimentally studied an impact of the surface oxide layer on quantum confinement effects (QCE) in Si quantum well (SQW) structures (surface-oxide/two-dimensional-Si/buried-oxide) with various surface oxide layer thickness TOX on silicon-on-insulator (SOI) substrate, by UV-Raman spectroscopy, photoluminescence (PL) method, and two-dimensional (2D) stress simulator. UV-Raman data show that tensile strain ε of SQW, stressed by a thermal expansion mismatch between surface oxide and Si layers, decreases with decreasing the TOX. According to the strain behavior in the SQW and strained-Si on strained-SOI, PL results show that bandgap EG of the SQW rapidly expands with decreasing TOX. As a result, we can estimate the EG of the fully relaxed SQW. However, QCE in SQW keep thermally stable, in spite of carrying out a high temperature N2 annealing process.

Self-consistent solution of Schrödinger–Poisson equations in a reverse biased nano-scale $$p$$ p - $$n$$ n junction based on $$\hbox {Si/Si}_{0.4}\hbox {Ge}_{0.6}/\hbox {Si}$$ Si/Si 0.4 Ge 0.6 / Si quantum well

Self-consistent solution of Schrödinger–Poisson equations in a reverse biased nano-scale $$p$$ p - $$n$$ n junction based on $$\hbox {Si/Si}_{0.4}\hbox {Ge}_{0.6}/\hbox {Si}$$ Si/Si 0.4 Ge 0.6 / Si quantum well

Quantum confinement in nonadditive space with a spatially dependent effective mass for Si and Ge quantum wells

We calculate the effect of a spatially dependent effective mass (SPDEM) [adapted from Costa Filho et al. (2011)] on an electron and a hole confined in a quantum well (QW). In the work of Costa Filho et al., the translation operator is modified to include an inverse character length scale, γ, which defines the SPDEM. The introduction of γ means that translations are no longer additive. In nonadditive space, we choose a ‘skewed’ Gaussian confinement potential defined by the replacement x→γ−1ln(1+γx) in the usual Gaussian potential. Within the parabolic approximation γ is inversely related to the QW thickness and we obtain analytic solutions to our confinement Hamiltonian. Our calculation yields a reduced dispersion relation for the gap energy (EG) as a function of QW thickness, D:EG~D−1, compared to the effective mass approximation: EG~D−2. Additionally, nonadditive space contracts the position space metric thus increasing the occupied momentum space and reducing the effective mass, in agreement with the relation: mo⁎−1∝∂2E/∂k2. The change in the effective mass is shown to be a function of the confinement potential via a point canonical transformation. Our calculation agrees with experimental measurements of EG for Si and Ge QWs.

Genetic design of enhanced valley splitting towards a spin qubit in silicon

The long spin coherence time and microelectronics compatibility of Si makes it an attractive material for realizing solid-state qubits. Unfortunately, the orbital (valley) degeneracy of the conduction band of bulk Si makes it difficult to isolate individual two-level spin-1/2 states, limiting their development. This degeneracy is lifted within Si quantum wells clad between Ge-Si alloy barrier layers, but the magnitude of the valley splittings achieved so far is small—of the order of 1 meV or less—degrading the fidelity of information stored within such a qubit. Here we combine an atomistic pseudopotential theory with a genetic search algorithm to optimize the structure of layered-Ge/Si-clad Si quantum wells to improve this splitting. We identify an optimal sequence of multiple Ge/Si barrier layers that more effectively isolates the electron ground state of a Si quantum well and increases the valley splitting by an order of magnitude, to ∼9 meV.

Effects of valence-band mixing and strain on thermoelectric properties of p-type quantum wells

Thermoelectric properties of p-type quantum wells (QWs) with flat subbands are investigated theoretically. The effects due to valence-band mixing and strain in QWs are considered in the calculation of electrical conductivity (σ), Seebeck coefficient (S), thermal conductivity, and figure of merit (ZT). It is found that the maximum ZT of QWs can be enhanced under strain. Such an enhancement of ZT results from the fact that the enhancement of S2 is stronger than the reduction of σ. The maximum values of ZT at room temperature can reach 0.55, 0.7, and 2.2 for GaAs, InAs, and InSb QWs with well width of 5 nm. For comparison, the ZT values of p-type silicon (Si) and germanium (Ge) QWs are also calculated. The optimal ZT values of Si and Ge QWs at room temperature can reach 0.21 and 0.3, respectively.

Nanoscale Distortions of Si Quantum Wells in Si/SiGe Quantum‐Electronic Heterostructures

Si quantum wells on plastically relaxed SiGe substrates have nanometer variations in crystallographic parameters crucial to quantum-information devices. Synchrotron X-ray nanodiffraction shows that the lattice of the Si quantum well varies in orientation and thickness over lateral distances of 100 nm to 1 μm. The result is that the energy levels of the confined states are shifted by energies similar to the electron temperature.

Experimental and theoretical analysis of the temperature dependence of the two-dimensional electron mobility in a strained Si quantum well

The temperature dependence of the mobility of the two-dimensional electron gas (2DEG) in a silicon quantum well strained by Si0.7Ge0.3 relaxed buffer layer is determined precisely by a mobility spectrum analysis. The 2DEG mobility is 2780 cm2/V s at room temperature and, upon cooling, increases continuously to reach μ2DEG=7.4×104cm2/Vs at 7 K. A back gate installed on the sample changes the 2DEG concentration n successfully to establish μ2DEG∝n1.4 at the constant temperature T=10K, implying that the scattering at such low temperature is limited solely by the remote ionized impurity scattering. Based on this finding, theoretical analysis of the temperature dependence of μ2DEG is performed based on the relaxation time approximation using 2DEG wavefunctions and subband structures determined self-consistently and including three major scatterings; by intravalley acoustic phonons, intervalley g-processes of longitudinal optical (LO) phonons, and remote ionized impurities. The calculation included only three fitting parameters, the shear deformation potential (Ξu=9.5eV), LO phonon deformation potential for g-process scattering (D0=9.0×108eV/cm), and sheet density of remote ionized impurities that have been determined by quantitative comparison with our experimental results. The temperature dependence of μ2DEG calculated theoretically show excellent agreement with experimentally determined μ2DEG.

Cyclotron resonance in the two-dimensional metallic phase of Si quantum wells

We have performed cyclotron resonance measurements on two-dimensional electrons near the metal-insulator transition. Both the cyclotron scattering time τCR and the transport scattering time τt decrease with the electron density. The values of τt/τCR are close to unity, indicating that the scattering mechanism does not depend on scattering angle in the metallic phase. Short-range potential fluctuations seem to play an important role in the appearance of the metallic behavior.

The diamagnetic susceptibility of hydrogenic donor in two-dimensional semiconductors with anisotropic effective mass of carriers

In this study, the effects of quantum confinement and effective mass anisotropy parameter on the diamagnetic susceptibility of a hydrogenic donor placed in GaAs, Si, and Ge quantum wells with infinite confinement potential are investigated in the effective mass and parabolic band approximations by using two and one parameter trial wave functions. It is observed that the diamagnetic susceptibility of a hydrogenic donor in anisotropic quantum wells is essentially equal to the transverse diamagnetic susceptibility part when well widths are larger than L>100Å, and the impurity is located at center. Moreover, a two parameter trial wave function model gives higher values of diamagnetic susceptibility, except for χz (GaAs).

Electron-phonon interaction effects on the direct gap transitions of nanoscale Si films

This study shows that the dielectric function of crystalline Si quantum wells (c-Si QW) is influenced by both carrier confinement and electron-phonon interactions. The energy shifts and lifetime broadening of the excitonic E1 direct gap transition of c-Si QWs from 2 to 10 nm are found to have a significant dimensional and temperature dependence that can be traced to changes in the phonon dispersion of nanoscale films. The influence of electron-phonon interactions on the dielectric function was verified by altering the phonon dispersion using different dielectric layers above a 5 nm c-Si QW.

The influence of the ionized impurity delta-layer potential in the quantum well on impurity binding energy

The influence of thermal ionization of an impurity delta-doped layer situated either in the center or on the edge of a quantum well (QW) on impurity binding energy is investigated theoretically for the case of Si0.8Ge0.2/Si QW. It is shown that the Hartree potential created by free electrons and by ionized impurities at high temperatures superimposes on the original (at low temperature) QW energy profile. Resulting new QWs have their own impurity binding energies. It is of interest that energies are nearly the same for center- and edge-doped QWs, contrary to those at low temperatures. The obtained results are explained on the basis of Coulomb’s law when decreasing the mean distance between free electron and impurity atom with temperature involves an increase in the impurity binding energy.

SiGe/Si quantum structures as a thermistor material for low cost IR microbolometer focal plane arrays

Uncooled microbolometer thermal infrared detector technology is presently revolutionizing the infrared technology field. Essential improvement of the cost/performance ratio would be achieved by microbolometer arrays with higher sensitivity, since this allows the use of simpler and less costly camera optics, which implies a lower cost of the complete IR camera. The sensitivity of the microbolometers depends critically on the signal-to-noise ratio of the integrated thermistor material, which is set by its temperature coefficient of resistance (TCR) and noise characteristics. In this work we have investigated the use of epitaxial silicon–germanium/silicon (SiGe/Si) quantum well (QW) structures as a thermistor material. Si 0.68Ge 0.32/Si QW structures typically give a TCR of 3.0%/K and low noise values. A calculation of the noise equivalent temperature NETD of a bolometer gives 25 mK using the following assumptions: f-number = 1, 30 Hz video frame rate for a 640 × 480 array, with a pixel size 25 × 25 μm. Higher TCR values are foreseen for SiGe/Si quantum dot structures, and the noise is expected to be similar to the QW based structures.