Simple Effective Mass Approximation Research Articles

Interplay between structural changes, surface states and quantum confinement effects in semiconducting Mg2Si and Ca2Si thin films.

Ab initio techniques have been used to investigate structural changes in semiconducting Mg2Si and Ca2Si thin films (from 17 nm down to 0.2 nm corresponding to the 2D structure) along with band-gap variations due to quantum confinement. Cubic Mg2Si(111) thin films being dynamically stable at thicknesses (d) larger than 0.3 nm displayed an indirect band gap, the reduction of which with increasing d could be reasonably well described by the simple effective mass approximation. Only 2D Mg2Si has a unique structure because of the orthorhombic distortion and the direct band gap. Since the surface energy of cubic Ca2Si(111) films was lower with respect to any surface of the orthorhombic phase, which is the ground state for the Ca2Si bulk, the metastable in-bulk cubic phase in the form of thin films turned out to be preferable in total energy than any orthorhombic Ca2Si thin film for d < 3 nm. Sizable structural distortion and the appearance of surface states in the gap region of Ca2Si thin films with d < 3 nm could be the reason for an odd dependence of the band-gap variation on d.

Electronic States in Cylindrical Core-Multi-Shell Nanowire

The recent advances in nanowire (NW) growth technology have made possible the growth of more complex structures such as core-multi-shell (CMS) NWs. We propose the approach for calculation of electron subbands in cylindrical CMS NWs within the simple effective mass approximation. Numerical results are presented for ${\rm GaAs/Al_{0.3}Ga_{0.7}As}$ radial heterostructure with AlGaAs-core and 4 alternate GaAs and AlGaAs shells. The influence of an effective mass difference in heterolayers is discussed.

Predictable spectroscopic properties of type-II ZnTe/CdSe nanocrystals and electron/hole quenching.

The spectroscopic properties of core/shell structured ZnTe/CdSe nanocrystals (NCs) have been systematically studied. By varying the ZnTe core diameter and the CdSe shell thickness, the absorption onset and the photoluminescence peak position of the ZnTe/CdSe NCs can be readily tuned over a wide range. The theoretical model based on an effective mass approximation demonstrates that the ZnTe/CdSe NCs have type II carrier localization in which the photoexcited electrons and holes are spatially separated and confined in the shell and core, respectively. The energetics of the conduction and valence bands and the bandgaps of the ZnTe/CdSe NCs are accurately predicted. The photoluminescent experiments show that electron quenchers having a large energy difference between their reduction potential and the lowest conduction band edge of the ZnTe/CdSe nanocrystals can completely quench the luminescence. Electron acceptors having a reduction potential only slightly below the conduction band edge partially quench the photoluminescence of the nanocrystals. In this case, the extent of quenching depends upon the thickness of the shell and the energy difference. Despite the confinement of photoexcited holes in the core, the photoluminescence could be still quenched by adsorbed hole quenchers. The extent of hole quenching depends upon the core size, the shell thickness and the oxidation potential of the quenchers. Basically, an increase in the core size and the shell thickness may lead to a decrease in the extent of hole quenching. The work presented here is of great interest since it can be extended to understand the spectroscopic properties and photoluminescence quenching behaviors of other core/shell semiconductor NCs.

Atomistic Tight-Binding Study of Contact Resistivity in Si/SiGe PMOS Schottky Contacts

The metal-semiconductor contact resistivity has started to play a critical role for the overall device performance as Si is reaching 10-nm size ranges. The International Technology Roadmap for Semiconductors (ITRS) target predicts a requirement of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-9</sup> Ω·cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> by 2023 which has been a challenging target to achieve. This paper explores the impact of doping concentration, Schottky barrier height, strain, and SiGe mole fraction on the resistivity of Si/SiGe p-type metal-oxide semiconductor (PMOS) contacts with 20-band atomistic tight binding quantum transport simulations. Commonly used simple effective mass approximation models are shown to overestimate the resistivity values. The predicted model results are compared with experimental data and the device parameters needed to achieve 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-9</sup> Ω·cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> are identified.

Tunneling current in HfO2 and Hf0.5Zr0.5O2-based ferroelectric tunnel junction

Ferroelectric tunnel junctions (FTJs) have been intensively explored for future low power data storage and information processing applications. Among various ferroelectric (FE) materials studied, HfO2 and H0.5Zr0.5O2 (HZO) have the advantage of CMOS process compatibility. The validity of the simple effective mass approximation, for describing the tunneling process in these materials, is examined by computing the complex band structure from ab initio simulations. The results show that the simple effective mass approximation is insufficient to describe the tunneling current in HfO2 and HZO materials, and quantitative accurate descriptions of the complex band structures are indispensable for calculation of the tunneling current. A compact k · p Hamiltonian is parameterized to and validated by ab initio complex band structures, which provides a method for efficiently and accurately computing the tunneling current in HfO2 and HZO. The device characteristics of a metal/FE/metal structure and a metal/FE/semiconductor (M-F-S) structure are investigated by using the non-equilibrium Green's function formalism with the parameterized effective Hamiltonian. The result shows that the M-F-S structure offers a larger resistance window due to an extra barrier in the semiconductor region at off-state. A FTJ utilizing M-F-S structure is beneficial for memory design.

Pseudo-potential band structure calculation of InSb ultra-thin films and its application to assess the n-metal-oxide-semiconductor transistor performance

The band structure of InSb thin films with ⟨1 0 0⟩ surface orientation is calculated using the empirical pseudopotential method (EPM) to evaluate the performance of nanoscale devices using a InSb substrate. Contrary to the predictions by simple effective mass approximation methods (EMA), our calculation reveals that the Γ valley is still the lowest lying conduction valley. Based on EPM calculations, we obtained the important electronic structure and transport parameters, such as effective mass and valley energy minimum, of InSb thin film as a function of the film thickness. Our calculations reveal that the ‘effective mass’ of Γ-valley electrons increases with the scaling down of the film thickness. We also provide an assessment of nanoscale InSb thin film devices using a non-equilibrium Green's function under the effective mass framework in the ballistic regime.

Band-edge diagrams for strained III–V semiconductor quantum wells, wires, and dots

We have calculated band-edge energies for most combinations of zincblende AlN, GaN, InN, GaP, GaAs, InP, InAs, GaSb and InSb in which one material is strained to the other. Calculations were done for three different geometries, quantum wells, wires, and dots, and mean effective masses were computed in order to estimate confinement energies. For quantum wells, we have also calculated band-edges for ternary alloys. Energy gaps, including confinement, may be easily and accurately estimated using band energies and a simple effective mass approximation, yielding excellent agreement with experimental results. By calculating all material combinations we have identified novel and interesting material combinations, such as artificial donors, that have not been experimentally realized. The calculations were perfomed using strain-dependent k-dot-p theory and provide a comprehensive overview of band structures for strained heterostructures.

Comparison between Quantum Confinement Effects of Quantum Wires and Dots

Dimensionality is an important governing factor in the electronic structures of semiconductor nanocrystals. The quantum confinement energies in one-dimensional quantum wires and zero-dimensional quantum dots are quite different. Using large-scale first-principle calculations, we have systematically studied the electronic structures of semiconductor (including group IV, III−V, and II−VI materials) surface-passivated quantum wires and dots. We have found that the band-gap energies of quantum wires and dots have the same scaling with diameter for a given material. The ratios of band-gap increases between quantum wires and dots are material-dependent, and for most direct band-gap materials, this ratio is very close to 0.586, as predicted by simple effective-mass approximation. We also have found a highly linear polarization of photoluminescence in quantum wires. The degree of polarization decreases with the increasing temperature and quantum wire size.

Study of Electron Transport in SOI MOSFETs Using Monte Carlo Technique with Full-Band Modeling

Effects of conduction-band non-parabolicity on electron transport properties in silicon-on-insulator (SOI) metal-oxide-semiconductor field effect transistors (MOSFETs) are studied by performing Monte Carlo simulation with a full-band modeling. An empirical pseudo-potential method is adopted for evaluating the two-dimensional electronic states in SOI MOSFETs. SOI-film thickness dependence of phonon-limited mobility, drift-velocity and subband occupancy is calculated and the results are compared with those of a simple effective mass approximation. The non-parabolicity effects are found to play an important role in 4-fold valleys under higher applied electric fields or at higher temperatures.

Optical transitions in silicon nanocrystals near structural transition region to amorphous silicon

Employing electroreflectance (ER) spectroscopy, we have studied optical transitions in Si nanocrystals with an emphasis on the relation between the optical transition energy and the mean crystal size. The ER features are observed between 1.1 and 3.1 eV arising from the optical transitions associated with the confined electron–hole (e–h) pairs. Interestingly, the lowest optical transition energy obtained from Si nanocrystals near structural transition region to amorphous Si are smaller than that found in Si nanocrystals with a mean crystal size of 1.3 nm. A systematic explanation in terms of a simple effective mass approximation (EMA) model has been done for the behavior.

Electroreflectance Study of Porous Silicon made from Substrates with Different Resistivities

AbstractEmploying electroreflectance (ER) spectroscopy, we have studied optical transitions in porous Si (PSi) with a thickness of 100±50 nm made from crystalline Si (c-Si) substrates with different resistivities, 4–10 ωcm (p-), 0.1–1 ωcm (p), and &lt; 0.018 ωcm (p+). The ER features observed at 1.1–2.8 eV in p+ PSi are analyzed with a simple effective mass approximation (EMA) model for confined electron-hole (e-h) pairs in a spherical quantum dot as we have previously done for those observed at 1.2–3.1 eV in p- PSi. From the ER analysis with the EMA model, the effective crystal size is estimated without destruction, and the kinetic energy and the Coulomb attraction energy of the confined e-h pairs are also deduced.Furthermore, the ER features corresponding to the optical transitions at E1(E0') critical point (CP) are observed at 2.8–3.3 eV in p+ PSi. With an increase in the crystal size, the transition energy of E1(E0') CP in p+ PSi is decreased, while that in p- and p PSi is unchanged from that of 3.4 eV found in c-Si including the p+c-Si. From the Raman results, strain- and disorder-induced spectral changes are found to be negligible, so that the high doping induced effect is the most acceptable mechanism for the red-shift in E1(E0') transitions of Si nanocrystals with the crystal size of 2–3 nm.

Electroreflectance Study of Light-Emitting Porous Silicon

ABSTRACTElectroreflectance spectroscopy measurements have been performed on light-emitting porous Si (LEPSi). The transmission electron microscope measurements reveal that LEPSi includes Si nanocrystals with a mean crystal size of 1–2 nm. The ER features are observed at a transition energy of 3.4 eV in all of the samples, giving that LEPSi still keeps the threedimensional (3D) electronic structure. Changes in the transition energies are not found for LEPSi with the different mean crystal sizes. Furthermore, we directly observed interband transitions of quantized states due to quantum-confined electron-hole (e-h) pairs in LEPSi as two or three extra ER features being located between 1.2 and 3.1 eV which are never observed in bulk crystalline Si. Employing a simple effective mass approximation model, we have evaluated the reduced mass, the kinetic energies and the Coulomb attraction energies of the quantumconfined e-h pairs. We also found that the energy distance between the transition energies at the ground state and the photoluminescence (PL) peak energies basically corresponds to the Coulomb attraction energies. Finally, we propose a new luminescent model based on interband transitions involving the quantum-confined dense e-h plasma.

Bound-to-extended state absorption in quantum wells confined byδ-like barriers

Within the framework of a simple envelope function and effective mass approximation, by including the spatial variation of effective mass and nonparabolicity effects, we have investigated the energy spectrum and intersubband optical absorption in a quantum well with additional thin and higher (δ -like) cladding barriers on either side of the well. The dependence of the absorption coefficient on the structure parameters, doping level, photon energy and temperature has been investigated. The absorption coefficient and spectrum strongly depend on the cladding barrier tunnel transparency. The peak absorption wavelength is shifted towards the high energies as the barrier transparency decreases. The temperature shift of the absorption peak is very small. The results are compared with experiments of Schneider et al. taking into account the broadening induced by well width fluctuations.

Excitonic Recombination and Relaxation in CdS Quantum Dots

Size-selective spectroscopic techniques and a tight-binding calculation with restricted configuration interaction are used to study the recombination and the relaxation of excitons in CdS quantum dots. The optical absorption spectrum is calculated and is found to be close to the experiments. The analysis of the luminescence shows that an emission of light corresponding to transitions between quantum confined states is obtained only in QDs larger than 3 nm. The exciton levels are compared with those given by simple effective mass approximation. The photoluminescence excitation spectra suggest that for upper exciton levels non-radiative captures of the carrier may become competitive compared to relaxation processes.

Conduction-band mixing in T- and V-shaped quantum wires

By means of a tight-binding approach, we have studied the influence of barrier states on the conduction band of the T- and V-shaped quantum wires. For AlAs/GaAs superlattices or pure AlAs barriers, $X$-related states induce strong modifications in the wire conduction band that cannot be accounted for by a simple effective-mass approximation. With respect to quantum wells, we show that the quasi-one-dimensional confinement of quantum wires enhances valley mixing and leads to a reduction in the energy of lower lying states.

Optical properties of ultrathin PbI 2 microcrystallite in polymer

We have prepared PbI 2 microcrystallites embedded in polymer, which have a layer structure and are ultrathin crystals consisting of two to nine monolayers. A very large energy shift of the exciton absorption band has been observed in these microcrystallites and interpreted in terms of size confinement of the translational motion of excitons in the c-direction perpendicular to the crystal surface. The simple effective mass approximation is broken down in 2, 3, 4 layer crystallites, because the crystal thickness is smaller compared to the exciton Bohr radius. Secondly, in the Raman spectrum where the excitation energy is resonant to the exciton energy, there appears a new line in the energy region below 20cm −1 which is characteristic of a ultrathin crystal. The Raman shift increases with decreasing the crystal thickness. This line is assigned as due to a longitudinal mode of a rigid-layer phonon. Thirdly, the confinement of the internal motion is studied by measuring a diamagnetic shift of the exciton energy in the magnetic field up to 150 T and a bound exciton luminescence in the ultrathin microcrystallites. Much larger binding energy of the exciton compared to the bulk value is estimated. This fact suggests that the envelope function of the exciton shrinks not only by a strong spacial restriction in the c-direction but also by the dielectric screening from the surrounding polymer. Fourthly, the exciton-phonon interaction is studied by the hole-burning measurement. From the temperature dependence of the hole width, it is suggested that the exciton is scattered by impurities or defects below 40 K and by a LO phonon above 40 K. Finally, the hydrostatic pressure dependence of the exciton energy and the resonant Raman scattering in the energy region of the optical phonons have been measured and the size effect on the atomic bonding between I and Pb is discussed. It is concluded that covalent bonding between Pb and I atoms changes to ionic bonding in the ultrathin crystallites.

Heavy Hole—Light Hole Splitting in GaAs/AlAs Superlattices

AbstractEppenga's six‐band k · p model for the description of the valence band structure of GaAs/AlAs quantum wells is modified for the k⟂ = 0 states in GaAs/AlAs superlattices. The model takes into account the coupling between the light holes and the spin—orbit split‐off holes and yields a very good agreement between experimental and calculated values of the splitting between the first heavy and light hole energy levels, which is not obtained in the simple effective mass approximation.

Spin—Orbit Splitting of the F-Center Band

Spin—orbit splitting of the first excited state of the F center is estimated in the simple effective-mass approximation. The splitting due to the outermost s orbitals of the atoms neighboring the vacancy in the crystal is related to the splitting of the p state in the free atom. As an example, spin—orbit splitting of the F center in cesium halides is estimated. It is found to 4-to-6 orders of magnitude too small to account for the structure observed in the F-center absorption band in cesium halides.