Pseudo-direct Gap Research Articles

Quasiparticle self-consistent GW band structures and phase transitions of LiAlO2 in tetrahedrally and octahedrally coordinated structures

A first-principles computational study is presented of various phases of LiAlO$_2$.The $\beta$ and $\gamma$ tetrahedral phases are found to be very close in energy with the $\gamma$ phase having the lowest energy. The octahedral $\alpha$ phase is a high-pressure phase and the transition pressure from the $\gamma$ and $\beta$ phases to $\alpha$ is determined to be about 1 GPa. The electronic band structures are determined using the quasiparticle self-consistent (QS) $GW$ method. The effective masses of the band edges and the nature of the band gaps are presented. The lowest energy $\gamma$ phase is found to have a pseudodirect gap of 7.69 eV. The gap is direct at $\Gamma$ but corresponds to a dipole forbidden transition. The imaginary part of the dielectric function and the absorption coefficient are calculated in the long-wavelength limit and the random phase approximation, without local field or electron-hole interaction effects for each phase and their anisotropies are discussed. Si doping on the Al site is investigated as a possible $n$-type dopant in $\gamma$-LiAlO$_2$ using a 128 atom supercell corresponding to 3.125 \% Si on the Al sublattice in the generalized gradient approximation and a smaller 16 atom cell with 25 \% Si in the QS$GW$ approximation. The Si is found to significantly perturb the conduction band and lower the gap but a clearly separated deep donor defect level is not found. However, the donor binding energy is still expected to be relatively deep, of order a few 0.1 eV in the hydrogenic effective mass approximation.

From pseudo-direct hexagonal germanium to direct silicon-germanium alloys

We present ab initio calculations of the electronic and optical properties of hexagonal ${\mathrm{Si}}_{x}{\mathrm{Ge}}_{1\ensuremath{-}x}$ alloys in the lonsdaleite structure. Lattice constants and electronic band structures in excellent agreement with experiment are obtained using density-functional theory. Hexagonal Si has an indirect band gap, whereas hexagonal Ge has a pseudo-direct gap, i.e., the optical transitions at the minimum direct band gap are very weak. The pseudo-direct character of pure hexagonal Ge is efficiently lifted by alloying. Already for a small admixture of Si, symmetry reduction enhances the oscillator strength of the lowest direct optical transitions. The band gap is direct for a Si content below 45 %. We validate lonsdaleite group-IV alloys to be efficient optical emitters, suitable for integrated optoelectronic applications.

Electron short-wave phonon scattering in crystals with chalcopyrite lattice

Electron short-wavelength phonon scattering is an effective channel for energy relaxation in crystals with a pseudo-direct optical gap. The equilibrium parameters of crystal structures and spectra of electrons and phonons in the ternary chalcopyrite compounds ZnSiP2 and ZnGeP2 are calculated self-consistently in good agreement with available experimental and theoretical calculations. The ab initio probabilities of phonon-assisted intervalley scattering of electrons in the conduction bands of the pseudo-direct-gap compounds ZnSiP2 and ZnGeP2 between the central Γ minima and the lowest lateral minima (valleys) at the T and N points have been calculated using the density functional perturbation theory. Electron–phonon scattering rates associated with intervalley phonons are calculated. Coupling constants for intervalley phonons in the chalcopyrite phosphides are close to their values in Si, Ge, and in the binary analog GaP.

Temperature enhanced spontaneous emission rate spectra in GeSn/Ge quantum wells

A GexSn1-x/Ge quantum well structure is studied by the 8-band k.p method. The band structures of both direct Γ valley and indirect L valley were calculated, and the relations between temperature and the spontaneous emission rate spectrum (SERS) were investigated. The results show an abnormal temperature dependent SERS phenomenon in the so-called pseudo-direct gap semiconductor. This can be explained by taking consideration of the contribution of electrons in the indirect L valley injecting into direct Γ valley under a higher temperature. Cases of higher Sn composition accompanied with larger compressive strain were investigated using the same model. The significant compressive strain effect compensates the dragging down of energy gap by the induced Sn atoms, which makes it difficult to achieve the transition from indirect band-gap material to direct band-gap material in quantum well devices.

Monolithically Integrated Ge-on-Si Active Photonics

Monolithically integrated, active photonic devices on Si are key components in Si-based large-scale electronic-photonic integration for future generations of high-performance, low-power computation and communication systems. Ge has become an interesting candidate for active photonic devices in Si photonics due to its pseudo-direct gap behavior and compatibility with Si complementary metal oxide semiconductor (CMOS) processing. In this paper, we present a review of the recent progress in Ge-on-Si active photonics materials and devices for photon detection, modulation, and generation. We first discuss the band engineering of Ge using tensile strain, n-type doping, Sn alloying, and separate confinement of Γ vs. L electrons in quantum well (QW) structures to transform the material towards a direct band gap semiconductor for enhancing optoelectronic properties. We then give a brief overview of epitaxial Ge-on-Si materials growth, followed by a summary of recent investigations towards low-temperature, direct growth of high crystallinity Ge and GeSn alloys on dielectric layers for 3D photonic integration. Finally, we review the most recent studies on waveguide-integrated Ge-on-Si photodetectors (PDs), electroabsorption modulators (EAMs), and laser diodes (LDs), and suggest possible future research directions for large-scale monolithic electronic-photonic integrated circuits on a Si platform.

Monolithic Ge-on-Si lasers for large-scale electronic–photonic integration

A silicon-based monolithic laser source has long been envisioned as a key enabling component for large-scale electronic–photonic integration in future generations of high-performance computation and communication systems. In this paper we present a comprehensive review on the development of monolithic Ge-on-Si lasers for this application. Starting with a historical review of light emission from the direct gap transition of Ge dating back to the 1960s, we focus on the rapid progress in band-engineered Ge-on-Si lasers in the past five years after a nearly 30-year gap in this research field. Ge has become an interesting candidate for active devices in Si photonics in the past decade due to its pseudo-direct gap behavior and compatibility with Si complementary metal oxide semiconductor (CMOS) processing. In 2007, we proposed combing tensile strain with n-type doping to compensate the energy difference between the direct and indirect band gap of Ge, thereby achieving net optical gain for CMOS-compatible diode lasers. Here we systematically present theoretical modeling, material growth methods, spontaneous emission, optical gain, and lasing under optical and electrical pumping from band-engineered Ge-on-Si, culminated by recently demonstrated electrically pumped Ge-on-Si lasers with >1 mW output in the communication wavelength window of 1500–1700 nm. The broad gain spectrum enables on-chip wavelength division multiplexing. A unique feature of band-engineered pseudo-direct gap Ge light emitters is that the emission intensity increases with temperature, exactly opposite to conventional direct gap semiconductor light-emitting devices. This extraordinary thermal anti-quenching behavior greatly facilitates monolithic integration on Si microchips where temperatures can reach up to 80 °C during operation. The same band-engineering approach can be extended to other pseudo-direct gap semiconductors, allowing us to achieve efficient light emission at wavelengths previously considered inaccessible.

Ge-on-Si optoelectronics

Electronic–photonic synergy has become an increasingly clear solution to enhance the bandwidth and improve the energy efficiency of information systems. Monolithic integration of optoelectronic devices is the ideal solution for large-scale electronic–photonic synergy. Due to its pseudo-direct gap behavior in optoelectronic properties and compatibility with Si electronics, epitaxial Ge-on-Si has become an attractive solution for monolithic optoelectronics. In this paper we will review recent progress in Ge-on-Si optoelectronics, including photodetectors, electroabsorption modulators, and lasers. The performance of these devices has been enhanced by band-engineering such as tensile strain and n-type doping, which transforms Ge towards a direct gap material. Selective growth reduces defect density and facilitates monolithic integration at the same time. Ge-on-Si photodetectors have approached or exceeded the performance of their III–V counterparts, with bandwidth-efficiency product >30GHz for p-i-n photodiodes and bandwidth-gain product >340GHz for avalanche photodiodes. Enhanced Franz–Keldysh effect in tensile-strained Ge offers ultralow energy photonic modulation with <30fJ/bit energy consumption and >100GHz intrinsic bandwidth. Room temperature optically-pumped lasing as well as electroluminescence has also been achieved from the direct gap transition of band-engineered Ge-on-Si waveguides. These results indicate that band-engineered Ge-on-Si is promising to achieve monolithic active optoelectronic devices on a Si platform.

(Invited) Band-Engineered Ge-On-Si Lasers for Integrated Photonics

Electronic-photonic synergy has become an increasingly clear solution to enhance the bandwidth and improve the energy efficiency of information systems. Monolithic lasers on silicon are ideal for large scale electronic-photonic integration. Germanium is a particularly interesting candidate for this application due to its pseudo-direct gap behavior in the near infrared regime for optical communications and compatibility with advanced silicon complementary metal oxide semiconductor (CMOS) technology. In this paper, we review theoretical modeling and experimental studies on optical gain and lasing from monolithic epitaxial Ge-on-Si devices band-engineered by tensile strain and n-type doping to compensate the energy difference between the direct and indirect conduction valleys. Demonstrations of optical gain and lasing at room temperature indicate that the Ge-on-Si laser is a promising candidate for monolithic electronic-photonic integrated circuits.

Ge-on-Si laser operating at room temperature

Monolithic lasers on Si are ideal for high-volume and large-scale electronic-photonic integration. Ge is an interesting candidate owing to its pseudodirect gap properties and compatibility with Si complementary metal oxide semiconductor technology. Recently we have demonstrated room-temperature photoluminescence, electroluminescence, and optical gain from the direct gap transition of band-engineered Ge-on-Si using tensile strain and n-type doping. Here we report what we believe to be the first experimental observation of lasing from the direct gap transition of Ge-on-Si at room temperature using an edge-emitting waveguide device. The emission exhibited a gain spectrum of 1590-1610 nm, line narrowing and polarization evolution from a mixed TE/TM to predominantly TE with increasing gain, and a clear threshold behavior.

GaAs/AlAs Superlattices and the Tight-Binding Model

A study of how well tight-binding models can reproduce the optoelectronic properties of GaAs/AlAs superlattices is carried out. It is shown that two key parameter sets lead to observable differences in the pseudo-direct energy gap regime, as well as in the direct gap regime. In addition to the differences in bulk fitting, other less direct differences, such as wave function localization, are found to play a role.

Interpretation of the dielectric function of porous silicon layers

The dielectric function of porous silicon layers depends strongly on the nanostructure of the silicon skeleton. In this paper we discuss the main effects, as determined from spectroscopic ellipsometric measurements of the dielectric functions of porous layers formed on p-doped material. Finite-size effects and the high inner surface area of the nanostructure lead to relaxation of k-momentum conservation as defined for infinite crystals and therefore to a broadening of the optical structure arising from interband critical points. In addition a small threshold energy shift is observed when the percolation of the structure is reduced. However, this shift is too small to explain red photoluminescence as a consequence of a pseudo-direct gap whose energy is blue-shifted by confinement.

Band structures, optical transition strengths and their pressure dependence of (GaP) n(AlP) n short-period superlattices with n=3 to 10

The electronic structure and optical transition strengths of (GaP) n(AlP) n short-period superlattices with the clean (001) interface (SL(n,n)) are calculated for n=3 to 10 using the first principle pseudopotential method within the local density approximation (LDA). The calculated results show that SL(n,n) are pseudo-direct gap semiconductors for n=3 to 10. The calculated optical transition strengths for the pseudo-direct gap transitions oscillate between even and odd n-values and those for even n-values are as strong as those of direct-gap-semiconductors, though the transition strengths decrease gradually with increasing n. In order to investigate the character of the pseudo-direct gap, the hydrostatic pressure dependence of the pseudo-direct band-gap energy and of the optical transition strength for SL(4,4) is also calculated. The result predicts that the band-gap becomes smaller, i.e. the absorption edge exhibits a red shift, and the optical transition strength decrease gradually by applying pressure and thus that the conduction band state at the fundamental absorption edge is the X z state folded into Г.

Towards a Microscopic Interpretation of the Dielectric Function of Porous Silicon

AbstractThe dielectric function of porous silicon layers depends strongly on the electronic properties of the nanostructure of the silicon skeleton. In this paper we discuss the main effects, as determined from spectroscopic ellipsometric measurements of the dielectric function of porous layers formed on p-doped material. Finite-size effects and the high inner surface area of the nanostructure lead to relaxation of k-momentum conservation as defined for infinite crystals and therefore to a broadening of the features in &lt;ε&gt; arising from interband critical points. In addition a small threshold energy shift is observed when the percolation of the structure is reduced. However, this shift is too small to explain red photoluminescence as a consequence of a pseudo-direct gap whose energy is blue-shifted by confinement.

Chemical shift and zone-folding effects on the energy gaps of GaAs-AlAs (001) superlattices.

The chemical shift and zone-folding effects obtained from quasiparticle calculations for ultrathin GaAs-AlAs superlattices are incorporated within a Kronig-Penny model for superlattices of the arbitrary lattice period. We determine that superlattices with lattice periods in the range of 3\ifmmode\times\else\texttimes\fi{}3 to 9\ifmmode\times\else\texttimes\fi{}9 have an X-derived pseudodirect gap. This result explains both the results from first-principles calculations for ultrathin superlattices and those from experiments for a broader lattice period.

Quasiparticle band gaps for ultrathin GaAs/AlAs(001) superlattices.

The quasiparticle band energies for 1\ifmmode\times\else\texttimes\fi{}1 and 2\ifmmode\times\else\texttimes\fi{}2 GaAs/AlAs(001) superlattices have been calculated from first principles using a self-energy approach. Both superlattices have indirect band gaps. The pseudodirect gaps at the zone center derived from folding of the Brillouin zone are larger than the direct gaps. The calculated results explain the various experimental data quantitatively. Matrix elements for optical transitions near the zone center show significant anisotropy. The effects of disorder on the observed spectra are discussed.

(111) oriented (GaAs)n(AlAs)n superlattices are direct band-gap materials for all n’s

Total energy calculations show that the (111) (AlAs)n(GaAs)n superlattice has a lower formation enthalpy (i.e., is stabler) than either the (001) or (110) superlattices. Self-consistent band structure calculations further show that while the (001) superlattice is direct only for n&amp;gt;7, the (111) superlattice has (i) a smaller and (ii) a direct (not pseudodirect) gap for all n’s. Contrary to the expectations based on particle in a box models, the confined states at the zone center are strongly localized even for the monolayer superlattice.

Photoluminescence and luminescence excitation spectra in ZnSiP2

Measurements of photoluminescence and luminescence excitation spectra of ZnSiP2 have been performed at 4.2K and two results were obtained. One is the observation of a new sharp emission line at 1.980 eV, due to the bound exciton associated with the pseudodirect gap. The other is the observation of another new series of absorption lines in the luminescence excitation spectrum of an emission line, at 1.984 eV, in addition to those reported previously. These results indicate that in ZnSiP2 radiative transitions occur at both the indirect and the pseudodirect gaps.

Observation of Luminescent Lines Related to Pseudodirect Gap in ZnSiP2 Crystals

The photoluminescence of ZnSiP2 crystals has been measured at 4.2 K. New sharp emission lines were observed at about 1.980 eV in a sample annealed at 400°C in vacuum. The intensity of these lines is greatly enhanced by excitation at the exciton absorption peak associated with the pseudodirect gap. This indicates that these emission lines are due to the bound excitons associated with the pseudodirect gap, in contrast to the results of previous photoluminescence measurements suggesting that this crystal is an indirect-gap semiconductor.

Pressure dependence of pseudodirect gaps in ZnGeP 2

The hydrostatic pressure dependence of pseudodirect gaps in ZnGeP 2 has been investigated at room temperature using a diamond anvil cell. The pressure coefficients of pseudodirect gaps between the lowest conduction band Γ 6 c and three valence bands (Γ 6 V, Γ 7 V, Γ 6 V) were −1.9 × 10 −6 eV/bar. These values are very close to that of the indirect gap (Γ 15 V−X 1 c) in A IIIB V semiconductors, as well as those in ZnSiP 2.

Pressure dependence of pseudo-direct gaps in ZnSiP 2

Hydrostatic-pressure dependence of pseudo-direct gaps in ZnSiP 2 has been measured at room temperature under pressures up to 23.6 kbar. The pressure coefficient of the lowest conduction band Γ c 6 is very close to that of the indirect X 1 band in A IIIB V semiconductors.