Z. Ikonić

Band structure calculations of Si-Ge-Sn alloys: achieving direct band gap materials

Alloys of silicon (Si), germanium (Ge) and tin (Sn) are continuously attracting research attention as possible direct band gap semiconductors with prospective applications in optoelectronics. The direct gap property may be brought about by the alloy composition alone or combined with the influence of strain, when an alloy layer is grown on a virtual substrate of different compositions. In search for direct gap materials, the electronic structure of relaxed or strained Ge1−xSnx and Si1−xSnx alloys, and of strained Ge grown on relaxed Ge1−x−ySixSny, was calculated by the self-consistent pseudo-potential plane wave method, within the mixed-atom supercell model of alloys, which was found to offer a much better accuracy than the virtual crystal approximation. Expressions are given for the direct and indirect band gaps in relaxed Ge1−xSnx, strained Ge grown on relaxed SixGe1−x−ySny and strained Ge1−xSnx grown on a relaxed Ge1−ySny substrate, and these constitute the criteria for achieving a (finite) direct band gap semiconductor. Roughly speaking, good-size (up to ~0.5 eV) direct gap materials are achievable by subjecting Ge or Ge1−xSnx alloy layers to an intermediately large tensile strain, but not excessive because this would result in a small or zero direct gap (detailed criteria are given in the text). Unstrained Ge1−xSnx bulk becomes a direct gap material for Sn content of >17%, but offers only smaller values of the direct gap, typically ≤0.2 eV. On the other hand, relaxed SnxSi1−x alloys do not show a finite direct band gap.

Band engineering and growth of tensile strained Ge/(Si)GeSn heterostructures for tunnel field effect transistors

In this letter, we propose a heterostructure design for tunnel field effect transistors with two low direct bandgap group IV compounds, GeSn and highly tensely strained Ge in combination with ternary SiGeSn alloy. Electronic band calculations show that strained Ge, used as channel, grown on Ge 1−xSnx (x > 9%) buffer, as source, becomes a direct bandgap which significantly increases the tunneling probability. The SiGeSn ternaries are well suitable as drain since they offer a large indirect bandgap. The growth of such heterostructures with the desired band alignment is presented. The crystalline quality of the (Si)Ge(Sn) layers is similar to state-of-the-art SiGe layers.

Self-consistent scattering theory of transport and output characteristics of quantum cascade lasers

Electron transport in GaAs/AlGaAs quantum cascade lasers operating in midinfrared is calculated self–consistently using an intersubband scattering model. Subband populations and carrier transition rates are calculated and all relevant electron-LO phonon and electron–electron scatterings between injector/collector, active region, and continuum resonance levels are included. The calculated carrier lifetimes and subband populations are then used to evaluate scattering current densities, injection efficiencies, and carrier backflow into the active region for a range of operating temperatures. From the calculated modal gain versus total current density dependencies the output characteristics, in particular the gain coefficient and threshold current, are extracted. For the original GaAs/Al0.33Ga0.67As quantum cascade structure [C. Sirtori et al., Appl. Phys. Lett. 73, 3486 (1998)] these are found to be g=11.3 cm/kA and Jth=6±1 kA/cm2 (at T=77 K), and g=7.9 cm/kA and Jth=10±1 kA/cm2 (at T=200 K), in good agreeme...

Intersubband electroluminescence from Si/SiGe cascade emitters at terahertz frequencies

The quantum cascade laser provides one possible method of realizing high efficiency light emitters in indirect band gap materials such as silicon. Electroluminescence results from Si/SiGe quantum cascade emitters are presented demonstrating edge emission from heavy-hole to heavy-hole transitions and light-hole to heavy-hole transitions. In surface-normal emission, only light-hole to heavy-hole electroluminescence is observed as predicted by theory. Intersubband emission is demonstrated at 2.9 THz (103 μm wavelength), 8.9 THz (33.7 μm), and 16.2 THz (18.5 μm) from the Si/SiGe quantum cascade heterostructures.

The direct and indirect bandgaps of unstrained SixGe1−x−ySny and their photonic device applications

Using empirical pseudopotential theory, the direct (Γ) and indirect bandgaps (L and X) of unstrained crystalline SixGe1−x−ySny have been calculated over the entire xy composition range. The results are presented as energy-contour maps on ternary diagrams along with a ternary plot of the predicted lattice parameters. A group of 0.2 to 0.6 eV direct-gap SiGeSn materials is found for a variety of mid-infrared photonic applications. A set of “slightly indirect” SiGeSn alloys having a direct gap at 0.8 eV (but with a smaller L-Γ separation than in Ge) have been identified. These materials will function like Ge in various telecom photonic devices. Hetero-layered SiGeSn structures are described for infrared light emitters, amplifiers, photodetectors, and modulators (free carrier or Franz-Keldysh). We have examined in detail the optimized design space for mid-infrared SiGeSn-based multiple-quantum-well laser diodes, amplifiers, photodetectors, and quantum-confined Stark effect modulators.

Terahertz imaging through self-mixing in a quantum cascade laser

We demonstrate terahertz (THz) frequency imaging using a single quantum cascade laser (QCL) device for both generation and sensing of THz radiation. Detection is achieved by utilizing the effect of self-mixing in the THz QCL, and, specifically, by monitoring perturbations to the voltage across the QCL, induced by light reflected from an external object back into the laser cavity. Self-mixing imaging offers high sensitivity, a potentially fast response, and a simple, compact optical design, and we show that it can be used to obtain high-resolution reflection images of exemplar structures.

Simulation and design of GaN/AlGaN far-infrared (λ∼34 μm) quantum-cascade laser

Designs of GaN/AlGaN quantum-cascade lasers emitting at 34 and 38 μm (ΔE∼36 and 34 meV) are presented, assuming either a- or c-plane crystal growth orientation. In the calculation of the quasibound state energies and wave functions, we account for the intrinsic electric field induced by piezoelectric and (in case of c-plane growth) the spontaneous polarization. The quantum-cascade structures were simulated, and their output characteristics extracted, using a fully self-consistent rate equation model with all relevant intra- and interperiod scatterings included. Both electron–LO-phonon and electron–electron scattering mechanisms are taken into account. Maximal population inversions between active laser states of up to 19% for the a-plane, and up to 40% for the c-plane design, are predicted and, based on estimated modal gain and waveguide/mirror losses in suitably designed structures, these indicate the feasibility of laser action in GaN/AlGaN cascades.

Interwell intersubband electroluminescence from Si/SiGe quantum cascade emitters

The quantum cascade laser provides one potential method for the efficient generation of light from indirect materials such as silicon. While to date electroluminescence results from THz Si/SiGe quantum cascade emitters have shown higher output powers than equivalent III–V emitters, the absence of population inversion within these structures has undermined their potential use for the creation of a laser. Electroluminescence results from Si/SiGe quantum cascade emitters are presented demonstrating intersubband emission from heavy to light holes interwell (diagonal) transitions between 1.2 THz (250 μm) and 1.9 THz (156 μm). Theoretical modeling of the transitions suggests the existence of population inversion within the system.

Mechanisms of dynamic range limitations in GaAs∕AlGaAs quantum-cascade lasers: Influence of injector doping

The influence of doping density on the performance of GaAs∕AlGaAs quantum-cascade lasers is presented. A fully self-consistent Schrodinger–Poisson analysis, based on a scattering rate equation approach, was employed to simulate the above threshold electron transport in laser devices. V-shaped local field domain formation was observed, preventing resonant subband level alignment in the high pumping-current regime. The resulting saturation of the maximal current, together with an increase of the threshold current, limits the dynamic working range under higher doping. Experimental measurements are in good agreement with the theoretical predictions.

Mechanisms of temperature performance degradation in terahertz quantum-cascade lasers

Electron transport in a terahertz GaAs/AlGaAs quantum-cascade laser is calculated using a fully self-consistent intersubband scattering model. Subband populations, carrier transition rates, and current densities are calculated and all relevant intra- and interperiod electron–electron and electron–LO-phonon scattering mechanisms are included. Employing an energy balance equation that includes the influence of both electron–LO-phonon and electron–electron scattering, the method also enables evaluation of the average electron temperature of the nonequilibrium carrier distributions in the device. In particular, the influence of the lattice temperature on the degradation of population inversion and device performance is investigated. The threshold currents, electric-field-current-density characteristics, and temperature-dependent performance are in good qualitative and quantitative agreement with measurement in a recent experimental realization [Kohler et al., Nature (London) 417, 156 (2002)]. Calculations ind...