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Superlattice

A superlattice is a periodic formed by alternating thin layers of two or more distinct materials, typically semiconductors, with each layer having a thickness on the scale of a few nanometers, resulting in an artificial crystal lattice with a periodicity much larger than the natural atomic spacing that modulates the electronic potential. This configuration arises from advanced epitaxial growth techniques, such as (MBE), which enable precise control over layer composition and thickness to create one-dimensional quantum confinement effects. The concept of semiconductor superlattices was theoretically introduced in 1970 by and Raphael Tsu at , who proposed a one-dimensional periodic potential in monocrystalline semiconductors achieved through periodic variations in composition, predicting the emergence of minibands and negative differential conductivity due to electron tunneling between layers. These structures exhibit quantized energy levels and modified band structures, leading to exceptional electronic, optical, and transport properties, including multistability from electric field domains and enhanced carrier mobilities. Notable applications encompass (QCLs) for tunable mid- to far- emission via intersubband transitions in GaAs/AlGaAs superlattices, high-performance photodetectors using type-II InAs/GaSb configurations for long-wavelength detection, and with improved figures of merit (e.g., ZT up to 2.4) for efficient cooling and power generation. Recent developments extend superlattices to two-dimensional van der Waals heterostructures and systems, broadening their use in strong light-matter interactions and advanced optoelectronic devices.

Fundamentals

Definition and Basic Principles

A is an artificially engineered periodic structure composed of alternating layers (or other geometries) of two or more distinct materials or phases, with individual layer thicknesses on the nanometer scale, forming a synthetic that exhibits properties distinct from those of the constituent bulk materials. This structure introduces an additional periodicity superimposed on the atomic-scale of the materials, enabling the design of novel electronic, optical, and mechanical behaviors through precise control of composition and layering. In , the foundational concept of a crystal involves the periodic repetition of atoms or unit cells, which gives rise to energy band structures via , where electron wavefunctions take the form of plane waves modulated by the periodic potential of the . Superlattices extend this periodicity to a larger scale, creating a modulated potential that folds the into minizones and generates minibands, leading to emergent properties such as modified and tunable band gaps. The periodic modulation of composition in a superlattice results in an artificial potential that can be generally expressed as
V(z) = V_0 + \sum_n V_n \cos\left( \frac{2\pi n z}{d} \right),
where V_0 is a constant offset, V_n are coefficients representing the strength of the periodic components, n is an , z is the direction perpendicular to the layers, and d is the superlattice period. This potential drives quantum confinement and coupling effects across layers, distinguishing superlattices from natural crystals.
Key characteristics of superlattices include layer thicknesses typically ranging from 1 to 100 , ensuring coherence lengths exceed the period to maintain quantum effects, as shorter scales (e.g., ~10 periods) were proposed in early designs to enable tunneling while preserving crystalline quality. Unlike random alloys or heterostructures, where atomic distributions are disordered and properties arise from statistical averaging, superlattices feature sharp, periodic interfaces that promote coherent wavefunction overlap and avoid localization from randomness. The interfaces are pivotal for property enhancement, as they facilitate and mechanisms, strain accommodation, and novel interfacial states that can dominate the overall functionality, such as reduced thermal conductivity or induced in otherwise insulating systems.

Historical Development

The concept of semiconductor superlattices was first proposed in 1970 by and Raphael Tsu at , who envisioned periodic structures of alternating thin layers of semiconductors to achieve negative conductivity through resonant tunneling between quantum wells. Their theoretical work, published in the IBM Journal of Research and Development, predicted the formation of minibands—narrow energy bands arising from the coupling of discrete quantum levels in adjacent wells—enabling novel electronic transport properties distinct from bulk materials. The first experimental realization of a superlattice occurred in 1974, when Esaki and Lester L. Chang fabricated a GaAs-AlAs structure using (), a technique that allowed precise control over layer thickness down to a few monolayers. This structure demonstrated the predicted negative differential resistance at , confirming the presence of miniband conduction and marking the transition from theory to practical synthesis. Esaki's earlier 1973 , shared with and for tunneling phenomena in semiconductors and superconductors, provided foundational insights into quantum effects that directly informed this breakthrough. During the 1980s, advancements in and other epitaxial techniques, such as metalorganic , enabled the growth of higher-quality superlattices with sharper and reduced defects, allowing direct observation of miniband dispersion through techniques like and optical . These improvements overcame initial challenges, including interface roughness and incorporation that broadened levels and obscured miniband features in early samples. By the late 1980s, such structures were routinely used to study quantum confinement effects, solidifying superlattices as a cornerstone of low-dimensional physics. Following these developments, research shifted post-2000 toward two-dimensional (2D) materials, where van der Waals heterostructures like formed moiré superlattices, extending the periodic layering concept to atomically thin systems with emergent properties such as correlated insulating states. This evolution built on the legacy while addressing scalability limits in traditional epitaxial growth.

Types of Superlattices

Semiconductor Superlattices

Semiconductor superlattices are periodic structures formed by alternating ultrathin layers of two or more materials with differing band gaps, creating a one-dimensional potential modulation that modifies the . A prototypical example is the GaAs/AlGaAs superlattice, where narrower-bandgap GaAs layers serve as quantum wells sandwiched between wider-bandgap AlGaAs barrier layers, enabling precise control over carrier confinement. These structures exhibit pronounced quantum confinement effects due to the nanoscale layer thicknesses, which quantize the energy levels of charge carriers in the growth direction, transforming continuous bulk bands into discrete subbands. Early experimental demonstrations of these effects in GaAs/AlGaAs superlattices laid the groundwork for research, revealing sharp excitonic absorption lines and confirming theoretical predictions of size-dependent energy shifts. Semiconductor superlattices are classified into subtypes based on the relative band s of the constituent materials. In Type I , both electrons and holes are confined within the same layer, as in GaAs/AlGaAs where the conduction and band edges of GaAs lie within the bandgap of AlGaAs. Type II features a staggered , spatially separating electrons and holes into different layers, exemplified by InAs/GaSb superlattices that promote long carrier lifetimes useful for . Type III involves a broken-gap , where the band maximum of one material exceeds the conduction band minimum of the other, as seen in PbTe/InSb systems enabling interband tunneling. Common material combinations include lattice-matched pairs like InP/InGaAs for minimal strain and pseudomorphic systems such as Si/Ge, where slight mismatches induce beneficial strain but require careful layer thickness control to avoid defects. Lattice matching is essential to maintain crystalline quality during epitaxial growth, limiting viable pairings to semiconductors with compatible lattice constants, typically within 0.5-1% mismatch.

Non-Semiconductor Superlattices

Non-semiconductor superlattices extend the periodic layering concept to metals, magnetic materials, dielectrics, and oxides, where behaviors emphasize metallic conduction, spin-dependent interactions, and strong correlations rather than bandgap . These structures exploit interfacial effects and interlayer to achieve tunable properties, such as modulated resistivity in metals and emergent magnetism in oxides, enabling applications in and correlated devices. Metallic superlattices feature alternating layers of noble or transition metals, promoting phenomena like (GMR) through spin-dependent electron scattering. In Fe/ superlattices, antiferromagnetic coupling across Cr spacers aligns Fe layer magnetizations antiparallel in zero field, suppressing conduction-electron transmission and yielding up to 100% resistance change under applied fields; this arises from interface-dominated spin-flip scattering rather than bulk magnetism. Similar / systems demonstrate interlayer coupling that alters dispersion and elastic moduli, with velocities increasing by 20-30% for modulation periods below 5 nm due to coherent effects. Plasmonic effects in these superlattices produce minibands of collective oscillations, splitting into symmetric and antisymmetric modes that enhance absorption and enable tunable optical metamaterials. Magnetic superlattices stack ferromagnetic layers with non-magnetic or antiferromagnetic spacers to harness , where exchange interactions dictate magnetization orientation and transport. Co/ multilayers exhibit perpendicular energies exceeding 2 MJ/m³, stemming from orbital hybridization at Co/ interfaces that favors out-of-plane moments over in-plane demagnetization; this enables dense, thermally stable bits in magnetic recording. Exchange bias in / double superlattices induces a unidirectional shift in the loop by up to 100 Oe, resulting from uncompensated antiferromagnetic at interfaces that pin the ferromagnetic layers during field reversal. These effects underpin spin-valve sensors, with resistance modulations supporting data read heads in hard drives. Dielectric and superlattices, often perovskite-based, probe correlated physics at insulating interfaces. SrTiO3/LaTiO3 structures confine 3d electrons in LaTiO3 layers against the SrTiO3 band , generating metallic with correlation-enhanced effective masses up to 5 times the bare value, as interfacial charge transfer creates a Mott-like state tunable by layer thickness. In cuprate variants like La1.84Sr0.16CuO4/SrLaMnO4, proximity to magnetic layers induces interfacial with Tc near 30 K, driven by charge redistribution and pair tunneling across non-superconducting barriers. Such systems reveal how periodic stacking amplifies emergent phases, including potential high-Tc enhancements via optimized interlayer coupling.

Fabrication and Materials

Common Materials

Superlattices are commonly constructed using semiconductor materials from the III-V, II-VI, and IV-IV groups, selected for their compatible lattice parameters that enable coherent epitaxial layering. In III-V , (GaAs) and (InAs) are frequently paired due to their direct bandgaps and lattice constants of 5.653 Å and 6.058 Å, respectively, with GaAs exhibiting a bandgap of 1.42 eV suitable for optoelectronic applications. These materials allow for type-I or type-II band alignments in superlattices, facilitating control over carrier confinement. Similarly, (InGaAs) variants are used for tunable bandgaps around 0.75 eV in infrared detectors. II-VI semiconductors such as zinc selenide (ZnSe) and (CdTe) are employed for wide-bandgap structures, particularly in blue-light emitters and . ZnSe has a of 5.668 and a direct bandgap of 2.67 , making it ideal for UV-visible when layered with GaAs substrates despite a ~0.3% mismatch. CdTe, with a of 6.481 and bandgap of 1.45 , is often combined with CdZnTe alloys to achieve strain-balanced superlattices for solar cells, though its toxicity limits some applications. IV-IV elemental semiconductors like silicon (Si) and germanium (Ge) form strained-layer superlattices valued for silicon-compatible electronics. Si has a lattice constant of 5.431 Å and indirect bandgap of 1.12 eV, while Ge's 5.658 Å constant and 0.66 eV bandgap enable miniband formation under ~4% mismatch strain, enhancing mobility in mid-infrared devices. These pairings exploit pseudomorphic growth on Si substrates to induce direct-like transitions. Beyond semiconductors, non-semiconductor materials expand superlattice functionalities into plasmonics, ferroelectrics, and thermoelectrics. Metals such as gold (Au) and silver (Ag) are used in metallic superlattices for plasmonic enhancement, leveraging their free-electron behavior and low optical losses in the visible range. Oxide-based superlattices often incorporate barium titanate (BaTiO3) for ferroelectric properties, with its perovskite structure enabling polarization switching in multilayer capacitors. Chalcogenides like bismuth telluride (Bi2Te3) are prominent in thermoelectric superlattices, where alternating layers reduce thermal conductivity while preserving electrical transport, achieving figures of merit up to ZT=2.4 at room temperature. Material selection seeks to minimize lattice mismatch, ideally below 1% for coherent epitaxial growth without significant strain, but strained-layer superlattices can accommodate higher mismatches (e.g., ~4% in ) through pseudomorphic growth, limiting dislocations up to the critical thickness. Thermal stability is critical, as layers must withstand processing temperatures up to 800°C without interdiffusion, favoring robust compounds like GaAs over more volatile ones. Toxicity considerations increasingly favor lead- and cadmium-free alternatives, such as InGaAs over CdTe, to comply with environmental regulations in commercial devices. Emerging two-dimensional van der Waals materials are gaining traction for flexible, atomically thin superlattices. stacked with hexagonal (hBN) forms moiré superlattices with tunable bandgaps up to 0.3 via twist angles, enabling correlated electron states. dichalcogenides like (MoS2) and (WSe2) create heterobilayer superlattices with type-II alignment, supporting interlayer excitons for and exhibiting moiré potentials that modulate optical properties.
MaterialGroupLattice Constant (Å)Bandgap (eV)Typical Application
GaAsIII-V5.6531.42
InAsIII-V6.0580.35 detectors
ZnSeII-VI5.6682.67UV emitters
CdTeII-VI6.4811.45
IV-IV5.4311.12 (indirect)
IV-IV5.6580.66Mid-IR devices

Production Techniques

Superlattices are primarily fabricated using epitaxial growth techniques that enable precise layer-by-layer deposition at the atomic scale. (MBE) is a cornerstone method, operating in conditions around 10^{-10} to minimize impurities and achieve atomic-layer precision. In MBE, elemental sources are evaporated from effusion cells to form molecular beams that impinge on a heated , with typical growth rates of 0.1-1 monolayers per second (ML/s) allowing for sharp interfaces essential to superlattice periodicity. This technique is widely used for superlattices, such as GaAs/AlAs structures, due to its ability to control composition and thickness with sub-monolayer accuracy. A complementary epitaxial approach is metalorganic chemical vapor deposition (MOCVD), a variant of (CVD) that employs metalorganic precursors and gases to deposit high-purity crystalline layers. MOCVD operates at atmospheric or low pressure, enabling scalable growth of III-V semiconductor superlattices like InAs/GaSb type-II structures on GaSb substrates. Unlike , it supports higher throughput but requires careful precursor flow control to maintain interface abruptness. Beyond epitaxial methods, is employed for metallic superlattices, where magnetron or dc deposits alternating metal layers in a environment. This technique suits materials like /W or /, producing multilayers with controlled thicknesses via sequential target switching. For oxide-based superlattices, (ALD) provides conformal, self-limiting growth using sequential precursor pulses, ideal for structures like HfO2/ZrO2 or organic-metal hybrids. ALD ensures uniform coverage even on complex substrates at temperatures below 400°C. Nanoparticle superlattices, in contrast, often rely on , where colloidal nanoparticles organize into ordered arrays driven by depletion forces or DNA grafting. This bottom-up method yields multicomponent lattices from heterodimers or particles. Fabrication success hinges on key process parameters, including substrate preparation, , and in-situ monitoring. Substrates like GaAs are typically cleaned and oxide-desorbed by heating to ~600°C in an flux prior to growth. Growth temperatures for GaAs-based superlattices in range from 500-700°C to promote two-dimensional layer-by-layer while avoiding interdiffusion. Reflection high-energy (RHEED) is routinely used to monitor and sharpness in real-time, ensuring abrupt transitions between layers. In the 2020s, advances have expanded superlattice production to larger scales and novel assemblies. Wafer-scale fabrication of van der Waals superlattices, such as Bi2Te3-Sb2Te3 chalcogenides, has been achieved via CVD, enabling uniform lateral and vertical heterostructures over centimeter areas. Roll-printing techniques have emerged for multilayer films, offering a one-step method for meter-scale vdW superlattices with precise stacking control. For 3D structures, one-step from molecular precursors during produces free-standing superlattices, bypassing multi-stage processes.

Physical Properties

Mechanical Properties

Superlattices exhibit enhanced stiffness attributable to their periodic layered structure, which introduces long-range coherency strains that stiffen the lattice beyond simple averages of constituent materials. In / superlattices, for instance, the longitudinal elastic constant C_{33} is approximately 13% higher than the Voigt-Reuss-Hill average of bulk and values, demonstrating anisotropic modulated by the bilayer period and interface quality. This enhancement arises from the superlattice periodicity constraining modes, leading to effective elastic moduli that vary with modulation wavelength. Plastic deformation in superlattices is governed by dislocation dynamics at layer interfaces, where misfit strains drive the nucleation and glide of dislocations to relieve lattice mismatch. The critical thickness h_c for pseudomorphic growth, beyond which misfit dislocations form, is described by the Matthews-Blakeslee model, which for edge dislocations is approximated as h_c = \frac{b (1 - \nu)}{8 \pi f (1 + \nu)} \ln \left( \frac{h_c}{b} \right), where b is the Burgers vector, \nu is Poisson's ratio, and f is the misfit strain. In Si/Ge superlattices, dislocation migration across coherent interfaces is significantly impeded by coherency stresses, resulting in velocities two orders of magnitude lower than in single-crystal Si or Ge, thereby stabilizing the structure against plastic flow. Interface effects in superlattices profoundly influence and through coherency strains that maintain structural integrity. Coherent s enhance by distributing , while promoting resistance to propagation; for example, in nitride-based superlattices, reaches up to 3.5 MPa\sqrt{m} at optimal bilayer periods due to barriers to pile-up. These strains also contribute to overall stability, preventing under load by balancing residual stresses across layers. Mechanical properties of superlattices are commonly assessed using , which probes and via localized deformation, revealing peak values exceeding 30 GPa in superlattices with periods around 6 nm. Brillouin scattering provides non-destructive measurement of elastic constants by analyzing acoustic velocities, confirming wavelength-dependent stiffening in Si/Ge systems without invasive contact.

Electronic and Optical Properties

Superlattices enable precise through quantum confinement and layer composition, allowing transitions from indirect to direct bandgaps in certain material systems. For instance, in / superlattices, strained layering can shift the conduction band minimum from the indirect X point to the direct Γ point, facilitating enhanced optical activity that is otherwise absent in bulk . This engineering arises from the periodic potential modulating the electronic states, resulting in tunable bandgaps that span visible to wavelengths depending on layer thicknesses and strain. Additionally, the effective mass of charge carriers is modified within minibands; along the growth direction, it increases due to the flattened dispersion relations, while in-plane masses remain closer to bulk values, altering carrier dynamics. The exhibits van Hove singularities at miniband edges, manifesting as sharp features that enhance electron-electron interactions and influence device performance. Optically, superlattices display enhanced binding energies compared to bulk materials, owing to reduced dimensionality that confines electron-hole pairs more tightly; in GaAs/AlGaAs systems, this enhancement can exceed the bulk value by factors of 2-3, leading to stable excitons at . Absorption spectra reveal distinct miniband transitions, appearing as step-like features or peaks corresponding to inter-miniband excitations, as observed in of GaAs/AlAs superlattices. can be tuned by adjusting layer thicknesses, shifting emission wavelengths through variations in quantization energy. Key effects include the , where applied electric fields induce red-shifts in absorption edges and quenching of due to spatial separation of electron-hole pairs, with shifts of several tens of meV in /AlN superlattices. In non-centrosymmetric superlattices, such as asymmetric / stacks, nonlinear optical processes like become prominent, enabling frequency doubling with efficiencies enhanced by the engineered symmetry breaking. Experimental probes of these properties include , which measures renormalized effective masses; in GaAs/AlGaAs superlattices, this technique reveals in-plane masses of approximately 0.067 m_e, confirming miniband influences. provides the complex dielectric function, capturing anisotropic responses and critical points associated with interband transitions in materials like GaAs/AlAs.

Theoretical Description

Band Structure and Minibands

In semiconductor superlattices, the periodic potential with a large period d (typically tens of nanometers) folds the bulk Brillouin zone into a smaller superlattice mini-Brillouin zone spanning from -\pi/d to \pi/d, resulting in the formation of narrow energy bands known as minibands separated by minigaps. This zone folding arises because the superlattice periodicity introduces a new reciprocal lattice vector $2\pi/d, which maps extended bulk states into the reduced zone, creating multiple minibands from the original conduction or valence bands. The discrete energy levels of unperturbed quantum well states in the infinite well limit scale approximately as E \approx \frac{\hbar^2 \pi^2}{2 m^* a^2} (with a the well width), but finite tunneling through barriers of thickness b broadens these into dispersive minibands whose width \Delta E decreases exponentially with b. Minibands form through the coupling of discrete quantum well states across adjacent wells via evanescent wave penetration of the barriers, leading to a splitting of degenerate levels into a band of allowed energies. In the tight-binding approximation, valid for thick barriers where well states are weakly overlapping, the miniband dispersion relation is given by E(k) = E_0 + 2t \cos(k d), where E_0 is the isolated well energy, t is the inter-well hopping amplitude (typically |t| \ll E_0), and k is the Bloch wavevector in the mini-Brillouin zone; the resulting bandwidth is $4|t|, with t determined by the barrier height and width. This cosine-like dispersion contrasts with the parabolic bulk bands and enables negative differential conductivity when the group velocity v_g = \frac{1}{\hbar} \frac{dE}{dk} = -\frac{2 t d}{\hbar} \sin(k d) peaks and then decreases with increasing energy. The (DOS) within each miniband exhibits a step-like profile, diverging as $1/\sqrt{|E - E_{\rm edge}|} at the band edges due to the one-dimensional-like along the growth direction, in contrast to the parabolic DOS of three-dimensional semiconductors. Minigaps between minibands suppress interband transitions, acting as effective barriers for motion perpendicular to the layers, while the overall DOS staircase structure enhances optical absorption at specific energies corresponding to miniband edges. Theoretical calculations of miniband structure often adapt the Kronig-Penney model to the superlattice's piecewise constant potential, solving the across well and barrier regions to yield the via the \cos(k d) = f(E), where f(E) is a involving continuity of wavefunction and at interfaces, determining allowed E(k) bands for |f(E)| \leq 1. This model captures finite barrier effects and provides accurate miniband widths and minigaps for parameters like GaAs/AlGaAs superlattices with d \approx 10 nm.

Bloch States and Wannier Functions

In semiconductor superlattices, the electronic wavefunctions are described by Bloch states adapted to the artificial periodicity of the layered structure. The standard Bloch theorem states that the wavefunction can be expressed as \psi_{\mathbf{k}}(\mathbf{r}) = e^{i \mathbf{k} \cdot \mathbf{r}} u_{\mathbf{k}}(\mathbf{r}), where u_{\mathbf{k}}(\mathbf{r}) is the periodic part with the periodicity, and \mathbf{k} is the wavevector in the . In superlattices, the larger period requires an envelope-function approximation, where the rapid oscillations within individual quantum wells are captured by the bulk Bloch functions u_n(\mathbf{r}) of the constituent materials, modulated by a slowly varying envelope function F(\mathbf{r}) that accounts for the interlayer coupling. Thus, the superlattice Bloch state takes the form \psi(\mathbf{r}) = \sum_n F_n(\mathbf{r}) u_n(\mathbf{r}), with the envelope satisfying an effective-mass derived from the superlattice potential. Wannier functions provide a localized real-space representation of these Bloch states, particularly useful for superlattices where spatial localization aids in modeling interlayer interactions. Defined via the Fourier transform, the Wannier function centered at lattice site \mathbf{R} is w_n(\mathbf{r} - \mathbf{R}) = \frac{1}{\sqrt{N}} \sum_{\mathbf{k}} e^{-i \mathbf{k} \cdot \mathbf{R}} \psi_{n\mathbf{k}}(\mathbf{r}), where the sum is over the N wavevectors in the Brillouin zone, and n labels the band. These functions form an orthonormal basis, satisfying \int w_m^*(\mathbf{r} - \mathbf{R}) w_n(\mathbf{r} - \mathbf{R}') d\mathbf{r} = \delta_{mn} \delta_{\mathbf{R}\mathbf{R}'}, which ensures their completeness and orthogonality across the superlattice. In theoretical models of superlattices, enable tight-binding approximations by representing the in terms of localized orbitals, facilitating calculations of hopping integrals between layers even in the presence of . This approach is advantageous for disordered superlattices, where the exponential localization of maximally localized simplifies the treatment of random potentials without relying on delocalized plane waves. find key applications in superlattice theory, such as schemes to compute from coarse \mathbf{k}-point grids, preserving topological invariants like Chern numbers essential for characterizing miniband structures. In disordered systems, they quantify the localization length \xi, defined as the decay rate of the Wannier function tail |w(\mathbf{r})| \sim e^{-|\mathbf{r}|/\xi}, providing insight into transitions within finite superlattices.

Transport Phenomena

Electron Transport

In semiconductor superlattices, electron transport occurs primarily through mechanisms that exploit the periodic potential, including sequential tunneling through barriers and coherent motion within minibands. Sequential tunneling dominates in weakly coupled systems where barriers are thick, allowing electrons to hop resonantly from one quantum well to the next when their energy aligns with the applied bias, leading to current peaks at specific voltages. In contrast, for moderately coupled superlattices, electrons undergo coherent transport across the structure, manifesting as Bloch oscillations under a uniform electric field F, with the oscillation frequency given by \omega_B = e F d / \hbar, where e is the electron charge, d is the superlattice period, and \hbar is the reduced Planck's constant; this frequency corresponds to the time for an electron to traverse the miniband in reciprocal space. Resonant tunneling in superlattices arises when the electron energy E matches the edges of the minibands, enabling enhanced transmission through the periodic barriers and resulting in sharp current peaks in the current-voltage characteristics. This process leads to negative differential resistance, where the current decreases with increasing voltage beyond the resonance, a hallmark predicted in early models of miniband conduction. The negative resistance stems from the saturation of the drift velocity as electrons align with the miniband's dispersion, limiting further acceleration by the field. The and in superlattices are governed by contributions from the minibands, with the conductivity expressed as \sigma = (e^2 \tau / m^*) \mathrm{DOS}(E_F) v^2, where \tau is the relaxation time, m^* is the effective mass, \mathrm{DOS}(E_F) is the at the E_F, and v is the velocity within the miniband; this formula highlights how limits the coherent transport and leads to negative differential when the field exceeds a where \tau becomes comparable to the Bloch . Experimentally, the Esaki-Tsu effect—negative differential conductivity due to miniband transport—has been demonstrated in GaAs/AlGaAs superlattices, showing current drops at fields around $10^3 V/, consistent with theoretical predictions for scattering times exceeding 1 ps. Time-resolved spectroscopy, such as emission measurements, has confirmed Bloch oscillations with periods matching \omega_B, observing coherent radiation at frequencies up to 1 in biased superlattices, providing direct evidence of the electron wavepacket dynamics over multiple periods.

Thermal and Phonon Transport

In superlattices, the periodic layering induces zone folding of the acoustic branches, where the of the superlattice is reduced compared to the bulk materials, leading to multiple folded branches within the new and the emergence of phonon bandgaps at the zone center and boundaries. These bandgaps arise from the interference of waves reflected at the interfaces, analogous to electronic minibands, and can suppress phonon propagation at specific frequencies, altering the overall vibrational . For instance, in GaAs/AlAs superlattices, folded longitudinal acoustic modes have been observed via , confirming the folding and associated gaps in the . The thermal conductivity in superlattices is significantly reduced due to enhanced at the interfaces, where with wavelengths comparable to the layer thickness experience , shortening the l. This follows the kinetic theory expression for lattice thermal conductivity: \kappa = \frac{1}{3} C v l where C is the specific heat per unit volume, v is the , and l is limited by interface scattering rather than bulk anharmonic processes. In superlattices, for example, interface scattering can reduce cross-plane thermal conductivity by over an compared to bulk values, approaching the amorphous limit for periods below 10 . Such reductions are crucial for applications requiring low heat transport while maintaining structural integrity. Thermoelectric performance in superlattices benefits from these phonon-blocking effects, which lower \kappa without proportionally degrading electrical conductivity, thereby enhancing the figure of merit ZT = S^2 \sigma T / \kappa, where S is the Seebeck coefficient, \sigma is electrical conductivity, and T is temperature. In Type II superlattices like EuTe/PbTe, quantum confinement at interfaces enhances the Seebeck coefficient by filtering low-energy carriers, increasing |S| up to 20% over bulk values at room temperature. A landmark example is p-type Bi₂Te₃/Sb₂Te₃ superlattices, where interface scattering yields \kappa \approx 0.5 W/m·K and power factors exceeding 30 × 10⁻³ W/m·K², achieving ZT \approx 2.4 at 300 K—nearly double the bulk alloy value. Thermal , the directional dependence of heat flow, can be engineered in graded superlattices where layer composition or thickness varies monotonically along the growth direction, creating asymmetric transmission. In such structures, propagating from low- to high-grading regions encounter fewer events than in the reverse direction, leading to rectification ratios up to 1.5 in 1D mass-graded models analogous to superlattice phononics. This asymmetry stems from the graded altering dispersion, enabling potential applications in nanoscale thermal diodes. Experimental characterization of these properties relies on techniques sensitive to phonon dynamics and heat flow. Time-domain thermoreflectance (TDTR) measures cross-plane thermal conductivity by monitoring transient temperature changes via reflectivity oscillations after ultrafast excitation, revealing interface-dominated in superlattices like Bi₂Te₃/Sb₂Te₃ with resolutions down to 10 nm periods. Complementarily, identifies folded modes and bandgaps through shifts in peak positions and intensities, as demonstrated in AlAs/GaAs superlattices where doublets from zone-folded acoustic branches confirm the superlattice periodicity. These methods provide direct verification of theoretical predictions without invasive probes.

Advanced Structures

Multidimensional Superlattices

Multidimensional superlattices extend the periodic layering of one-dimensional (1D) structures into higher spatial dimensions, introducing lateral or volumetric periodicity that alters electronic and optical behaviors. In superlattices, periodicity occurs primarily in the plane, creating lateral modulation distinct from the vertical stacking typical of 1D systems. For instance, arrays, such as those formed by CdTe and CdSe nanoparticles, self-assemble into binary structures like AlB₂ or MgZn₂ phases when the effective radius ratio is tuned to values around 0.5–0.8, enabling ordered lateral arrangements with interparticle spacings of 5–10 nm. These configurations contrast with vertical modulation by confining carriers in the plane, leading to miniband formation primarily along in-plane directions. Three-dimensional (3D) superlattices achieve volumetric periodicity through stacking of nanoparticle layers or direct of multicomponent units, resulting in isotropic or near-isotropic properties in cubic lattices. Examples include binary assemblies of (Au) and (Fe₃O₄) nanoparticles forming NaZn₁₃-type structures, where 3.8 nm Au cores cluster icosahedrally around 13.4 nm Fe₃O₄ particles in a body-centered cubic arrangement with lattice constants of approximately 20 nm. Similarly, core-shell nanoparticles can be incorporated into 3D volumetric stacks, enhancing charge separation for optoelectronic applications. Photonic crystals serve as optical analogs to these electronic 3D superlattices, featuring periodic contrasts that create photonic bandgaps analogous to electronic minibands. The properties of multidimensional superlattices often exhibit anisotropic in due to directional periodicity, where effective masses differ along in-plane versus out-of-plane axes, as seen in Dirac-based superlattices with elliptic or hyperbolic shapes. In configurations, can become more isotropic in symmetric lattices like NaCl-type assemblies (packing ~0.79), allowing uniform in all directions, though persists in layered stacks. Emergent topological states arise in oxide superlattices, such as (SrTaO₃)₁/(SrIrO₃)₁, through d-d inversion and spin-orbit coupling, yielding strong topological insulators with ~20 meV gaps and Z₂ invariants of (1;001), protected by crystal symmetries. Fabrication of multidimensional superlattices faces challenges in achieving long-range order over large areas, particularly in controlling defects during assembly. via templates enables precise 3D positioning; for example, 6-helix bundle DNA structures electrostatically bind 2.5 nm Au nanoparticles into tetragonal superlattices with lattice parameters a = 9.25 nm and c = 12.5 nm, though mismatches in size or lead to disordered aggregates. -induced methods, such as slow drying of dispersions on substrates, promote superlattice in stages—from dilute to concentrated phases—yielding rhombohedral assemblies with high order at evaporation rates of 0.07 μm/s, but faster rates introduce cracks and defects due to capillary stresses.

Hybrid and Moiré Superlattices

Hybrid superlattices combine layered two-dimensional () or three-dimensional () materials with inorganic components, such as perovskites, to create structures with tunable properties. These systems often form natural multiple quantum wells through alternating and inorganic layers, enabling precise control over interlayer spacing via rational design of molecular constituents. For instance, in 2D -inorganic perovskites (OIHPs), the organic spacers can be engineered to adjust the , facilitating tunable responses that influence dynamics and charge separation. This layering approach enhances optoelectronic performance by modulating the spatial variability of properties across the and inorganic interfaces. Moiré superlattices emerge from twist-induced periodic patterns in stacked materials, such as or transition metal dichalcogenides (TMDs), where a small relative generates a superlattice potential. In twisted bilayer (TBG), the of approximately 1.1° flattens the electronic bands, leading to narrow bandwidths around the charge neutrality point and enabling strong electron correlations. These flat bands, with bandwidths on the order of tens of meV, isolate low-energy states and promote interaction-driven physics, as observed in both fully and partially relaxed structures. Similar moiré patterns in /TMD heterostructures extend these effects to valley-dependent phenomena. Emergent quantum properties in these superlattices arise from enhanced electron-electron interactions in the flat bands. In moiré TBG, correlated Mott-like insulating states appear at half-filling (ν = ±2 electrons per moiré ), with activation gaps around 0.32 meV below 4 K, signaling strong repulsion dominating . emerges nearby, with critical temperatures of 0.3–1.8 K in doping-dependent domes, potentially involving unconventional spin-triplet pairing that persists under magnetic fields up to 10 T. Additionally, the has been observed at three-quarter filling in slightly twisted TBG (θ ≈ 1.2°), manifesting as orbital with Hall resistances exceeding 10⁴ Ω due to interlayer scattering and . These phenomena, first noted in late experiments and confirmed through studies, highlight moiré systems as platforms for correlated quantum matter. Recent developments in 2024–2025 have advanced designable through and moiré architectures. In systems, modular electrostatic co-assembly has enabled the creation of over 50 distinct organic-inorganic superlattices using anionic clays and cationic polymers, offering customizable periodicities for quantum applications. Room-temperature -3D systems, integrating defects in hBN and , achieve enhanced magnetic sensing with coupling strengths up to 78 kHz, paving the way for scalable quantum technologies. For moiré superlattices, ultrasensitive optoelectronic biosensor arrays based on twisted integrate detection with Au nanodisks, achieving detection limits below 1 for biomolecules via moiré-enhanced plasmonics. These innovations underscore the potential for tailored superlattices in quantum simulation and sensing.

Applications

Optoelectronics and Quantum Devices

Superlattices, particularly those based on GaAs/AlGaAs heterostructures, have enabled the development of quantum cascade lasers (QCLs) that emit in the mid-infrared range through inter-miniband transitions. In these unipolar devices, electrons cascade through a series of quantum wells and barriers, where is achieved between upper and lower minibands within the conduction band, facilitated by resonant tunneling and for depopulation. The operating principle relies on engineered layer thicknesses to control the energy spacing of minibands, allowing emission wavelengths typically between 3 and 12 μm. Tunability in GaAs/AlGaAs QCLs is achieved by varying the quantum well widths and barrier compositions, which adjust the inter-miniband transition energies, enabling broadband operation or single-mode emission via distributed feedback gratings. These lasers operate at for mid-IR wavelengths and have been pivotal for applications in and sensing due to their high output powers. Wall-plug efficiencies can reach up to 27% at in optimized InP-based designs, though GaAs/AlGaAs systems exhibit lower efficiencies, up to 5% in continuous-wave mode at , due to interface quality limitations. In optoelectronic detection, superlattices support THz detectors leveraging resonant tunneling, where sequential tunneling through minibands in GaAs/AlGaAs structures enables coherent response up to 1 THz, transitioning from classical to quantum detection at higher frequencies. For modulation, electro-optic devices based on n-i-p-i doping superlattices in GaAs utilize the Franz-Keldysh effect, where an applied tilts the band edges, enhancing sub-bandgap and achieving high contrast ratios. These modulators exhibit response times on the order of picoseconds, limited by carrier sweep-out . For quantum devices, superlattices contribute to structures exploiting Wannier-Stark localization, where an applied creates localized states in GaAs/AlGaAs structures. Additionally, magnetic superlattices, such as Fe/V heterostructures, form spin valves that exhibit , enabling spin-dependent transport for processing. These configurations demonstrate superconducting proximity effects, with critical current modulation up to 50% in F/S/F trilayers.

Energy Conversion and Sensing

Superlattices have emerged as key materials in energy conversion technologies, particularly in thermoelectrics and , where their engineered band structures and interfaces enable efficient charge and heat management. In thermoelectric applications, / superlattices reduce through enhanced at periodic interfaces, achieving reductions of up to 92% compared to nanowires, which boosts the (ZT) for converting to . For instance, /SiGe superlattices exhibit Seebeck coefficients up to 300 μV/K at , enabling integrated energy harvesters for autonomous sensors. analogues like BiCuSeO superlattices further optimize performance via dual vacancies that lower to 0.37 W m⁻¹ K⁻¹ and yield ZT values of 0.84 at 750 K, rising to ~1.4 with doping. Piezoelectric superlattices also facilitate mechanical-to-electrical energy conversion by coupling elastic and responses across layered structures, allowing frequency-selective . Measurements of in such systems reveal distinct bands for acoustic-to-electrical conversion, with coupling coefficients exceeding 20% in optimized Pb(Zr,Ti)O₃-based superlattices. In photovoltaics, type-II superlattices like InAs/GaSb enhance charge separation via staggered band alignments, supporting broadband absorption from visible to short-wave wavelengths. For sensing, superlattices excel in detection through intersubband transitions in quantum wells, as in type-II InAs/GaSb/AlSb structures that achieve cut-off wavelengths of ~2.4 μm at 300 and detectivities of 4.72 × 10¹⁰ cm Hz¹/² W⁻¹. These devices operate via photo-generated carrier extraction without high bias, minimizing dark current to 5.3 × 10⁻⁴ A/cm² at . Organic-inorganic covalent superlattices, such as AgBDT, enable temperature-compensated gas sensing by ratiometric comparison of photoelectric and gas responses, reducing variation from 21.81% to 7.81% over 25–65°C and detecting NO₂ at limits of 0.22 ppb. Their multi-quantum well design yields on/off ratios of 1769 at 475 nm for photoelectric sensing and responses of 15000% to 100 ppm NO₂. Seminal work by Kroemer on heterostructure band-edge discontinuities laid the foundation for these superlattice-based sensors and converters.

References

  1. [1]
    Superlattice - an overview | ScienceDirect Topics
    A superlattice is a special type of thin-film, which refers to a periodic structure of layers of two (or more) materials.
  2. [2]
    Semiconductor Superlattices - an overview | ScienceDirect Topics
    Semiconductor superlattices consisting of alternating layers of two semiconductors with different energy bands were conceived by Esaki and Tsu more than 37 ...
  3. [3]
  4. [4]
    Theory of semiconductor superlattice electronic structure
    Jan 1, 1990 · The authors review the theory of semiconductor superlattice electronic structure. First a survey of theoretical methods is presented.
  5. [5]
  6. [6]
  7. [7]
    Monolayer Semiconductor Superlattices with High Optical Absorption
    Jun 17, 2024 · Our results demonstrate that monolayer superlattices are a powerful platform directly applicable to improve strong light-matter coupling.
  8. [8]
  9. [9]
    New Transport Phenomenon in a Semiconductor "Superlattice"
    Aug 19, 1974 · We report electronic transport properties in a GaAs-AlAs periodic structure known as a "superlattice" prepared by a molecular-beam epitaxy.Missing: AlGaAs MBE
  10. [10]
  11. [11]
    Superlattice and Negative Differential Conductivity in Semiconductors
    We consider a one-dimensional periodic potential, or “superlattice,” in monocrystalline semiconductors formed by a periodic variation of alloy composition.
  12. [12]
    None
    ### Summary of Band Alignment Types in Semiconductor Heterostructures
  13. [13]
    Quantum confinement effects in semiconductors (Chapter 3)
    In this chapter we describe size-dependent optical properties of semiconductor nanostructures related to quantum confinement.
  14. [14]
    A review of recent advances in semiconductor superlatticesa
    I. INTRODUCTION. Activities in semiconductor superlattices have expanded greatly in recent years with advances achieved both in scope and in depth.
  15. [15]
    [PDF] Chapter 1 - Type-II Superlattice Infrared Detectors
    Three types of band alignment are available in this material system: (1) type-I (nested) band alignment between GaSb and AlSb, (2) type-II staggered alignment ...
  16. [16]
    EuTe/PbTe Superlattices: Mbe Growth and Optical Characterization
    Feb 21, 2011 · In such superlattices the wide band gap EuTe layers act as barriers and the narrow band gap PbTe as quantum wells. The superlattices were ...
  17. [17]
    A simple lattice-matching guide for superlattices and ...
    We give simple guidelines for lattice matching of tetrahedrally bonded semiconductors, including II–VI and III–V compounds, group-IV elements, and Mn ...Missing: common | Show results with:common
  18. [18]
    Giant Magnetoresistance of (001)Fe/(001)Cr Magnetic Superlattices
    Nov 21, 1988 · We ascribe this giant magnetoresistance to spin-dependent transmission of the conduction electrons between Fe layers through Cr layers.Missing: metallic | Show results with:metallic
  19. [19]
    Brillouin scattering from Love waves in Cu/Nb metallic superlattices
    Aug 31, 1987 · Love waves have been observed for the first time by Brillouin scattering. The c12 constant of the metallic superlattice Cu/Nb has been ...
  20. [20]
    Evolution and splitting of plasmon bands in metallic superlattices
    Jul 15, 1989 · The band structure and the band gaps were found to be sensitive to the relative thickness of insulating layers that separate two metallic layers ...
  21. [21]
    Strong perpendicular magnetic anisotropy in [Co/Pt]n ultrathin ...
    Dec 20, 2016 · In the superlattices, a low sputtering power and high Ar sputtering pressure were used to deposit Co and Pt sublayers to reduce the intermixing ...
  22. [22]
    Magnetic configurations in exchange-biased double superlattices
    Dec 27, 1999 · The layer-by-layer magnetization of a “double-superlattice” Fe/Cr(211) exchange-bias junction was determined by polarized neutron ...
  23. [23]
    Superconductivity at Interfaces in Cuprate‐Manganite Superlattices
    May 10, 2023 · This research demonstrates the presence of high-T c superconducting La 1.84 Sr 0.16 CuO 4 in direct proximity to SrLaMnO 4 and provides evidence for the ...
  24. [24]
    [PDF] I. GaAs Material Properties
    Lattice thermal conductivity. 0.55 W/cm-°C. Dielectric constant. 12.85. Band gap. 1.42 eV. Threshold field. 3.3 kV/cm. Peak drift velocity. 2.1 × 107 cm/s.
  25. [25]
    [PDF] Intermediate Band Solar Cells Based on InAs Quantum Dots ...
    The lattice mismatch between InAs (lattice constant = 6.0564 Å) and GaAs (lattice constant = 5.6532 Å) causes strain to accumulate. This accumulated strain ...
  26. [26]
  27. [27]
    [PDF] Characterization Of Cadmium Zinc Telluride Solar Cells
    Nov 12, 2003 · Cadmium Telluride (CdTe) forms crystals in zincblende structure with a lattice parameter of 6.48. Each Cd atom is tetrahedrally surrounded by ...
  28. [28]
    [PDF] Fabrication and characterization of single crystal CdTe ... - UIC Indigo
    where aT is the lattice constant (Å) at T°C. The lattice constant of the cubic zincblende CdTe is. 6.481 Å at room temperature and its bonding length is ...<|separator|>
  29. [29]
    A Theoretical Simulation of the Radiation Responses of Si, Ge ... - NIH
    May 2, 2018 · The Displacement Events in Bulk Silicon and Germanium. The lattice constant of bulk Si is determined to be 5.50 Å, which agrees well with the ...
  30. [30]
    Next-generation electronics by co-design with chalcogenide materials
    Oct 9, 2025 · Chalcogenides such as the transition-metal dichalcogenides (e.g., NbSe2, TiSe2) and tetradymite topological insulators (e.g., Bi2Te3, Bi2Se3) ...
  31. [31]
    Superlattice Engineering on 2D Bi2Te3‐Sb2Te3 Chalcogenides
    Apr 7, 2025 · These periodic low‐dimensional structures consist of alternating layers of different materials (typically semiconductors or metals) arranged in ...Missing: common non-
  32. [32]
    Influence of Lattice Mismatch on Structural and Functional ... - NIH
    Sep 2, 2023 · The mostly used parameter to quantify the strain in hetero-epitaxial layer architectures is the lattice mismatch α = ( a s − a f ) / a s between ...Missing: criteria superlattice stability
  33. [33]
    Interlayer couplings, Moiré patterns, and 2D electronic superlattices ...
    Jan 6, 2017 · By using direct growth, we create a rotationally aligned MoS2/WSe2 hetero-bilayer as a designer van der Waals heterostructure.
  34. [34]
    Moiré-engineered light-matter interactions in MoS2/WSe2 ... - Nature
    Oct 9, 2024 · Moiré superlattices formed with monolayers of two-dimensional (2D) materials offer a new degree of freedom (moiré lattice constant or moiré ...
  35. [35]
    (PDF) Molecular Beam Epitaxy: Thin Film Growth and Surface Studies
    Aug 6, 2025 · The vacuum requirements for the MBE process are typically better than 10 ⁻¹⁰ torr. This makes it possible to grow epitaxial films with high ...
  36. [36]
    Molecular Beam Epitaxial Growth and Structures of Al/Ag Superlattices
    C, at a growth rate of 0.1 monolayers per second, on 50-nm-thick (100) Ag buffer layers preformed on (100) MgO substrates. In situ reflection high-energy ...
  37. [37]
    Effects of growth conditions on the GaAs/AlAs superlattices by ...
    The GaAs/AlAs superlattices were prepared by molecular beam epitaxy (MBE) at different growth temperatures (500 degrees C, 600 degrees C and 660 degrees C) ...
  38. [38]
    Metalorganic Chemical Vapor Deposition of III-V Semiconductors
    MOCVD is a process in which two or more metalorganic chemicals (for instance, trimethylgallium) or one or more metalorganic sources and one or more hydride ...
  39. [39]
    Metalorganic chemical vapor deposition growth of InAs/GaSb type II ...
    Feb 28, 2012 · Abstract. InAs/GaSb type II superlattices were grown on (100) GaSb substrates by metalorganic chemical vapor deposition (MOCVD).
  40. [40]
    Metal-Organic Chemical Vapor Deposition - ScienceDirect.com
    MOCVD is defined as a variant of chemical vapor deposition (CVD) used for creating high purity crystalline semiconducting thin films and micro/nano structures, ...
  41. [41]
    Structural and magnetic studies of Fe/W metallic superlattices ...
    We have sputter deposited Fe/W superlattices on several types of substrates using magnetically enhanced dc sputtering guns. The deposition rates were ...
  42. [42]
    Superconducting metallic superlattices - NASA/ADS
    A brief description of our sputtering technique used to prepare superlattices consisting of Nb/Cu and Ta/Mo is given. Optical interferometry, X ray diffraction, ...
  43. [43]
    Atomic Layer Deposition of HfO2/ZrO2 Superlattices - MediaHub
    Sep 24, 2024 · Atomic Layer Deposition (ALD) is used to build up the superlattice, we use ALD because it provides uniform and precisely tuned thickness, then ...
  44. [44]
    Atomic layer deposition of functional multicomponent oxides
    Nov 1, 2019 · Atomic layer deposition (ALD) is a low-temperature (<400 °C) and low-vacuum (10 −2 to 10 mbar) chemical gas-phase deposition technique.
  45. [45]
    Self-Assembly of Atomically Aligned Nanoparticle Superlattices from ...
    Mar 13, 2023 · We demonstrate that heterodimers consisting of two conjoined NPs can self-assemble into novel multicomponent SLs with a high degree of alignment between the ...Introduction · Results and Discussion · Conclusions · References
  46. [46]
    Superlattice assembly strategy of small noble metal nanoparticles ...
    Apr 30, 2024 · The self-assembly of noble metal nanoparticles is a process that involves the spontaneous organization of these particles into ordered ...
  47. [47]
    How to growth your first sample: Oxide remove - Dr. Faebian Bastiman
    Dec 2, 2013 · Once you have found the oxide remove temperature, hold the substrate there for 10 minutes. You can even go 10-20°C higher at this stage without ...<|separator|>
  48. [48]
    MBE growth and RHEED characterization of MnSe/ZnSe ...
    It is important to clarify the growth condition of ZB MnSe for preparing high quality MnSe/ZnSe superlattices. In this paper, we describe the MBE growth of MnSe ...
  49. [49]
    One-step preparation of three-dimensional superlattices during ...
    Mar 4, 2025 · The one-step method involves direct, spontaneous self-assembly of 3D nanoparticle superlattices during nanoparticle growth in synthesis ...
  50. [50]
    Influence of the short-range structural properties on the elastic ...
    The elastic constant tensor of Sim / Gen superlattices with different modulation wavelengths has been determined by Brillouin light scattering spectroscopy. The ...
  51. [51]
  52. [52]
    Mechanistic study of superlattice-enabled high toughness and ...
    Aug 18, 2020 · To conclude, the concept of enhanced mechanical properties due to superlattice architectures has been shown in multiple studies. Together with ...
  53. [53]
    Mechanical properties of epitaxial TiN/(V0.6Nb0.4)N superlattices ...
    Nov 1, 1992 · We have used nanoindentation to measure the mechanical properties of epitaxial TiN/(V0.6Nb0.4)N superlattices, grown on MgO(100), ...
  54. [54]
    Genetic-Algorithm Discovery of a Direct-Gap and Optically Allowed ...
    Jan 12, 2012 · We provide an unexpected solution to this classic problem, by spatially melding two indirect-gap materials (Si and Ge) into one strongly dipole-allowed direct- ...
  55. [55]
    Dipole-allowed direct band gap silicon superlattices - Nature
    Dec 11, 2015 · In this work, we report low-energy pure Si-based superlattices that exhibit direct and optically allowed band gaps with good lattice matching with c-Si.
  56. [56]
    Electron Mass Tunneling along the Growth Direction of (Al,Ga) As ...
    Jun 23, 1986 · We have measured the effective mass of electrons tunneling through thin barriers in (Al, Ga) As/GaAs superlattices by performing cyclotron-resonance ...
  57. [57]
    Photoluminescence of superlattices and a study of minibands
    Mar 13, 2007 · The effective heavy-hole mass was taken to be linearly temperature dependent, ... According to Weiler 17 the only parameter that changes ...
  58. [58]
    Scaling of exciton binding energy and virial theorem in ...
    Jan 15, 1999 · We reexamine this subject by calculating the exciton binding energy and the corresponding virial theorem value in quantum wells and wires with infinite ...
  59. [59]
    Phys. Rev. B 48, 1601 (1993) - Infrared absorption in superlattices
    Jul 15, 1993 · Infrared spectroscopy is used to study optical transitions between the two lowest minibands in strongly coupled n-type GaAs/AlxGa1−xAs ...
  60. [60]
    [1402.3081] Screening of the quantum-confined Stark effect in AlN ...
    Feb 13, 2014 · Screening of the quantum-confined Stark effect in AlN/GaN nanowire superlattices by Germanium doping. We report on electrostatic screening of ...
  61. [61]
    Limitations to the realization of noncentrosymmetric ${\mathrm{Si}}_ ...
    Sep 15, 1994 · Here we report second-harmonic generation induced by a 775-nm beam on several samples of nominally (Si7Ge3)20 SLS's grown on several substrates ...
  62. [62]
    Comparison between the electronic dielectric functions of a GaAs ...
    Jul 15, 1995 · Comparison between the electronic dielectric functions of a GaAs/AlAs superlattice and its bulk components by spectroscopic ellipsometry using ...
  63. [63]
    Superlattice and Negative Differential Conductivity in Semiconductors
    Aug 9, 2025 · We consider a one-dimensional periodic potential, or “superlattice,” in monocrystalline semiconductors formed by a periodic variation of alloy composition.
  64. [64]
    Miniband parameters of semiconductor superlattices - ScienceDirect
    Miniband parameters for a semiconductor superlattice are worked out using a Kronig Penney type of model potential distribution in the individual layers, ...
  65. [65]
    [PDF] 1. INTRODUCTION
    In general, the mass of an electron in a superlattice is roughly one order of magnitude larger than typical effective masses of bulk crystals, while widths of ...
  66. [66]
    Superlattices | Theory of Optical Processes in Semiconductors
    One finds that the step-like density of states of N QWs is retained, when the miniband width t i goes to zero and as such E i = E 0i. A plot of ρ sl(E) ...
  67. [67]
    A tunneling measurement of the electronic density of states of a ...
    We report on electrical tunneling measurements into strongly coupled superlattices which have allowed us to probe the full density of states. The samples, grown ...
  68. [68]
    Sequential tunneling current through semiconductor superlattices ...
    A calculation within the framework of the Bardeen Hamiltonian has been performed to evaluate the tunneling current through the superlattice in the presence of ...
  69. [69]
    Coherent submillimeter-wave emission from Bloch oscillations in a ...
    May 24, 1993 · We directly detect the coherent electromagnetic radiation originating from Bloch oscillations of charge carriers in an electrically biased semiconductor ...
  70. [70]
    Coherent phonons in superlattices | Phys. Rev. B
    May 7, 2007 · This is analogous to electronic energy gaps; band gaps in the phonon-dispersion relation are formed at the center and at the boundary of the ...
  71. [71]
    [PDF] Folded Acoustic and Quantized Optic Phonons in Semiconductor ...
    Sep 2, 2025 · acoustic phonons in superlattices. 3 ) The dispersion is given by d dI aid2. 1+K 2 wd wd2 cos qd - cos(-) cos(-) sin (-. ) sin (-). (14) which ...
  72. [72]
    Folded-acoustic phonons in GaAs/AlAs thin-layer superlattices ...
    Aug 15, 1989 · We have measured the pressure dependence (0–18 GPa) of folded-acoustic-phonon and confined-optic-phonon frequencies in thin-layer GaAs/AlAs ...Missing: paper | Show results with:paper
  73. [73]
    Thermal conductivity of semiconductor superlattices: Experimental ...
    Apr 16, 2009 · We present thermal conductivity measurements performed in three short-period ( GaAs ) 9 ⁢ ( AlAs ) 5 superlattices.Missing: seminal | Show results with:seminal
  74. [74]
    Thermal rectification in graded materials | Phys. Rev. E
    Jul 3, 2012 · In order to identify the basic conditions for thermal rectification we investigate a simple model with nonuniform, graded mass distribution.Missing: superlattices | Show results with:superlattices
  75. [75]
    Study of phonons in semiconductor superlattices by Raman ...
    Raman spectroscopy is used to study phonons in a series of thin (AlAs)m/(GaAs)n superlattices (SLs) grown by molecular beam epitaxy (MBE).
  76. [76]
    Structure Direction of II−VI Semiconductor Quantum Dot Binary ...
    We report a nanoparticle radius ratio dependent study of the formation of binary nanoparticle superlattices (BNSLs) of CdTe and CdSe quantum dots.
  77. [77]
    Structural diversity in binary superlattices self-assembled ... - Nature
    Dec 2, 2015 · Here we show the formation of 10 different binary nanocrystal superlattices (BNSLs) with both two- and three-dimensional order.<|separator|>
  78. [78]
    Laser-Induced Fabrication of Au@CdS Core−Shell Nanowires
    Dec 13, 2010 · Au@CdS core−shell nanowires have been fabricated readily by exciting the surface-plasmon resonances of gold nanospheres, which were priorly ...
  79. [79]
    Topological phase transitions in superlattice based on 2D Dirac ...
    Highlights. Superlattice based on 2D Dirac crystals with anisotropic dispersion is studied. Electron dispersion is obtained for considered superlattice. ...
  80. [80]
    Emergent topological states via digital (001) oxide superlattices
    Sep 29, 2022 · Our work demonstrates how to induce non-trivial topological states in (001) perovskite oxide heterostructures by rational design.
  81. [81]
    DNA origami directed 3D nanoparticle superlattice via electrostatic ...
    Feb 21, 2019 · Molecular self-assembly using DNA is a compelling approach to construct structurally versatile, well-defined and highly addressable nano- and ...
  82. [82]
    Superlattice growth and rearrangement during evaporation-induced ...
    Jun 5, 2017 · In this study, we follow the evaporation induced self-assembly of iron oxide nanoparticle superlattices by real-time in-situ small angle X-ray ...Introduction · Methods · Saxs And Gisaxs
  83. [83]
    Organic-inorganic hybrid perovskites and their heterostructures
    Dec 7, 2022 · Hybrid 2D perovskites are natural multiple quantum wells consisting of alternative organic and inorganic layers.
  84. [84]
    Dielectric Engineering of 2D Organic–Inorganic Hybrid Perovskites
    ### Summary of Dielectric Engineering in 2D Organic-Inorganic Hybrid Perovskites
  85. [85]
    Tunable Interlayer Delocalization of Excitons in Layered Organic ...
    We present an in-depth study of the energy and spatial distribution of the lowest-energy excitons in layered organic–inorganic halide perovskites.
  86. [86]
    Correlated states in magic angle twisted bilayer graphene under the ...
    Aug 13, 2020 · Insulating and superconducting states appear upon doping magic angle twisted bilayer graphene (TBG), and there is evidence of correlation induced effects.
  87. [87]
    Correlated insulating and superconducting states in twisted bilayer ...
    Twistronics (1–7), the use of the relative twist angle between adjacent van der Waals layers to produce a moiré superlattice and flat bands, has emerged as a ...
  88. [88]
    How Magical Is Magic-Angle Graphene? - ScienceDirect.com
    May 6, 2020 · The magic angles are a discrete set of angles (with the largest one around 1.1°) at which the twisted bilayer graphene exhibits a unique electronic structure.
  89. [89]
    Exotic quantum phenomena in twisted bilayer graphene - IOPscience
    Sep 4, 2025 · Twisted bilayer graphene at the magic angle shows superconductivity, correlated Mott-like insulating states, and orbital ferromagnetism.<|separator|>
  90. [90]
    [PDF] Room-Temperature Hybrid 2D-3D Quantum Spin System for ... - arXiv
    Apr 15, 2025 · Abstract. Advances in hybrid quantum systems and their precise control are pivotal for devel- oping advanced quantum technologies.Missing: biosensor | Show results with:biosensor
  91. [91]
    Ultrasensitive optoelectronic biosensor arrays based on twisted ...
    Aug 23, 2025 · This study pioneers an opto-electronic biosensor by synergizing twist-engineered moiré superlattices in graphene with CRISPR technology,
  92. [92]
    GaAs/AlxGa1−xAs quantum cascade lasers | Applied Physics Letters
    A unipolar injection quantum cascade (QC) laser grown in an AlGaAs/GaAs material system by molecular beam epitaxy, is reported.
  93. [93]
    Room temperature quantum cascade lasers with 27% wall plug ...
    Aug 6, 2025 · Room temperature quantum cascade lasers with 27% wall plug efficiency ... The GaAs-based GaAs/AlGaAs material system is generally used to ...
  94. [94]
    THz response of GaAs/AlGaAs superlattices - ScienceDirect.com
    The sequential tunneling superlattices show a transition from classical rectification at frequencies below 600 GHz to quantum response above 1 THz. In the ...
  95. [95]
    High speed and high contrast electro-optical modulators based on ...
    High speed and high contrast electro-optical modulators based on n-i-p-i doping superlattices ... Modulator Based on the Franz-Keldysh Effect. 1993, IEEE ...
  96. [96]
    High contrast electro-optic n-i-p-i doping superlattice modulator
    Below the band-gap energy the absorption changes are entirely due to the Franz-Keldysh tails in the intrinsic and the space charge regions of the structure. As ...
  97. [97]
    Interaction between Wannier-Stark states in semiconductor ...
    Aug 15, 1994 · We examine the interaction between the Wannier-Stark ladders derived from two minibands in a semiconductor superlattice.Missing: qubits | Show results with:qubits
  98. [98]
    Superconducting spin valves based on epitaxial Fe/V superlattices
    Oct 15, 2008 · In the F1/S/F2-type spin valves the ferromagnetic layer F1 was either a [Fe/V] or a superlattice, the F2 layer was a Fe-, a Co-, or a film.
  99. [99]
    Ultra-low Thermal Conductivity in Si/Ge Hierarchical Superlattice ...
    Nov 16, 2015 · In this paper, we demonstrate using molecular dynamics simulations that the already low thermal conductivity of Si/Ge SNW can be further reduced ...
  100. [100]
    Ge/SiGe superlattices for thermoelectric energy conversion devices
    Aug 7, 2025 · The materials and devices are aimed at integrated energy harvesters for autonomous sensing applications. We report Seebeck coefficients up ...
  101. [101]
    Bulk Superlattice Analogues for Energy Conversion
    Among the various applications, this review focuses on two selected applications: energy storage and electromagnetic interference shielding. Moreover, new ...
  102. [102]
    Energy conversion in piezoelectric superlattices - SPIE Digital Library
    By measuring the S parameters, the coupling behavior is observed and the frequency bands corresponding to different kinds of energy conversion can be identified ...Missing: applications | Show results with:applications
  103. [103]
    Type–II superlattices base visible/extended short–wavelength ...
    Mar 21, 2019 · The various superlattices that make up the structure are all lattice matched to the GaSb substrate to within 1000 ppm, which is in agreement ...
  104. [104]
    Organic-inorganic hybrid covalent superlattice for temperature ...
    Feb 12, 2025 · We develop a ratiometric-gas sensing method that leverages the exceptional photoelectric and chemiresistive gas sensing sensitivity of organic-inorganic hybrid ...