Growth variation effects in SiGe-based quantum cascade lasers

Epitaxial growth of SiGe quantum cascade (QC) lasers has thus far proved difficult, and nonabrupt Ge profiles are known to exist. We model the resulting barrier degradation by simulating annealing in pairs of quantum wells (QWs). Using a semiclassical charge transport model, we calculate the changes in scattering rates and transition energy between the lowest pair of subbands. We compare results for each of the possible material configurations for SiGe QC lasers. The effects are most severe in n-type (001) Si-rich systems due to the large effective electron mass, and in p-type systems due to the coexistence of light holes and heavy holes. The lower effective mass and conduction band offset of (111) oriented systems minimizes the transition energy variation, and a large interdiffusion length (Ld = 1.49 nm) is tolerated with respect to the scattering rate. Ge-rich systems are shown to give the best tolerance with respect to subband separation (Ld = 3.31 nm), due also to their low effective mass

n-Type Si/SiGe quantum cascade structures

Detail, looking up at figure of Mickiewicz; Adam Bernard Mickiewicz (1798-1855) was a Polish poet, publisher and political writer of the Romantic period. Mickiewicz was active in the struggle to achieve independence for Poland (from Russia) and so lived in exile. He settled first in Rome, later in Paris, where he became professor of Slavic literature at the Collège de France. Mickiewicz is depicted on top of the column as a pilgrim, with his left arm raised. Source: Wikipedia; http://en.wikipedia.org/wiki/Main_Page (accessed 5/7/2011

Intervalley mixing and intersubband transitions in n-type Si/SiGe quantum wells

The Si/SiGe materials system offers the prospect of excellent integration between CMOS technology and optoelectronics, employing well-established fabrication technology at low cost. Whilst the indirect bandgap means that interband lasing is challenging, stimulated emission from intersubband transitions offers a route to long wavelength Si based lasers. In bulk silicon, the conduction band minima are located in six degenerate valleys near the Brillouin zone edge in the directions. In a two-dimensional system however, uniaxial strain effects split the degeneracy of the valleys into two sets — two z valleys perpendicular to the heterostructure interfaces and four xy valleys in the growth plane. Atomistic simulation methods have shown that the two degenerate valley sets are sufficiently separated from each other to be considered independently within an effective mass approximation (EMA) model. Electrons emanating transversely from each of the xy valleys contribute identically to the z-varying component of the wavefunction, resulting in four degenerate states. In the case of the z valleys however, the electrons have different wavevector components in the z-direction. Quantum confinement yields interference between these basis functions and two distinct solutions to Schr¨odinger’s equation exist at separate energies, i.e. the degeneracy of z states is split. The effect has been observed experimentally in Schubnikov-de Haas oscillations in high magnetic fields.[1] It is therefore important to consider the mixing effect between the z valleys when determining states in a quantum confined system. Whilst atomistic simulation methods such as the tightbinding approximation implicitly take intervalley mixing into account,[2] the computation is considerably slower than the effective mass approximation — particularly in the case of large complicated structures such as a quantum cascade laser (QCL). A Double Valley Effective Mass Approximation (DVEMA) is therefore desirable as it offers the rapid computation of the EMA whilst including intervalley mixing effects explicitly. Such a model was derived for a square quantum well by Ting and Chang.[3] The energy splitting in the lowest states is shown to be a decaying oscillatory function of well width. The present work details the expansion of the DVEMA model to a general symmetric envelope potential. In SiGe molecular beam epitaxy (MBE), interdiffusion of Ge between heterolayers prevents abrupt interfaces from existing in the envelope potential. By considering a number of structures with more realistic interfaces than previous studies, the surface segregation effect is shown to reduce valley splitting slightly. Although the DVEMA applies only to symmetric structures, the present studies show that the model often remains reliable for slightly asymmetric structures. Using the DVEMA model, the effect of valley splitting upon realistic Si/SiGe intersubband optical devices has been investigated. The optical matrix elements for valley split intersubband transitions are shown to be almost identical, whilst their energies may differ by up to 10 meV. The emission spectrum is therefore expected to exhibit transition doublets when the valley splitting becomes large. It is shown that through careful design, the valley splitting may be minimized; although there is scope for exploiting intervalley scattering effects to achieve population inversion in an intersubband laser

Nonequilibrium electron heating in inter-subband terahertz lasers

Inter-subband laser performance can be critically dependent on the nature of the electron distributions in each subband. In these first Monte Carlo device simulations of optically pumped inter-subband THz lasers, we can see that there are two main causes of electron heating: intersubband decay processes, and inter-subband energy transfer from the "hot" nonequilibrium tails of lower subbands. These processes mean that devices relying on low electron temperatures are disrupted by electron heating, to the extent that slightly populated subbands can have average energies far in excess of the that of either the lattice or other subbands. However, although these heating effects invalidate designs relying on low temperature electron distributions, we see that population inversion is still possible in the high-THz range at 77 K in both stepped and triple-well structures, and that our 11.7 THz triple-well structure even promises inversion at 300 K. © 2002 American Institute of Physics

Simulated [111] Si-SiGe terahertz quantum cascade laser

The prospect of developing a silicon laser has long been an elusive goal, mainly due to the indirect band gap and large effective carrier masses. We present a design for a terahertz intersubband laser grown on the [111] crystal plane and simulate performance using a rate equation method including scattering due to alloy disorder, interface roughness, carrier-phonon and Coulombic interactions. We predict gain greater than 40 cm-1 and a threshold current density of 70 A/cm2

Design of Ge/SiGe quantum-confined Stark effect electroabsorption heterostructures for CMOS compatible photonics

We describe a combined 6×6 k.p and one-band effective mass modelling tool to calculate absorption spectra in Ge–SiGe multiple quantum well (MQW) heterostructures. We find good agreement with experimentally measured absorption spectra of Ge–SiGe MQW structures described previously in the literature, proving its predictive capability, and the simulation tool is used for the analysis and design of electroabsorption modulators. We employ strain-engineering in Ge–SiGe MQW systems to design structures for modulation at 1310 nm and 1550 nm

Substrate orientation and alloy composition effects in n-type SiGe quantum cascade structures

We show using a theoretical self-consistent effective mass/rate equation approach that n-type SiGe-based quantum cascade lasers are potentially made viable by either using the (111) orientation or a Ge-rich substrate

The importance of electron temperature in silicon-based terahertz quantum cascade lasers

Quantum cascade lasers (QCLs) are compact sources of coherent terahertz radiation. Although all existing QCLs use III-V compound semiconductors, silicon-based devices are highly desirable due to the high thermal conductivity and mature processing technology. We use a semiclassical rate-equation model to show that Ge/SiGe THz QCL active region gain is strongly enhanced by reducing the electron temperature. We present a bound-to-continuum QCL design employing L-valley intersubband transitions, using high Ge fraction barriers to reduce interface roughness scattering, and a low electric field to reduce the electron temperature. We predict a gain of similar to 50 cm(-1), which exceeds the calculated waveguide losses. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3237177

Three-dimensional Inkjet Printed Solid Oxide Electrochemical Reactors. I. Yttria-stabilized zirconia Electrolyte

Solid oxide fuel cell (SOFC) and electrolyser (SOE) performances can be enhanced significantly by increasing the densities of (electrode | electrolyte | pore) triple phase boundaries and improving geometric reproducibility and control over composite electrode | electrolyte microstructures, thereby also aiding predictive performance modelling. We developed stable aqueous colloidal dispersions of yttria-stabilized zirconia (YSZ), a common SOFC electrolyte material, and used them to fabricate 2D planar and highly-customisable 3D microstructures by inkjet printing. The effects of solids fraction, particle size, and binder concentration on structures were investigated, and crack-free, non-porous electrolyte planes were obtained by tailoring particle size and minimising binder concentration. Micro-pillar arrays and square lattices were printed with the optimised ink composition, and a minimum feature size of 35 μm was achieved in sintered structures, the smallest published to-date. YSZ particles were printed and sintered to a 23 μm thick planar electrolyte in a Ni-YSZ|YSZ|YSZ-LSM|LSM electrolyser for CO2 splitting; a feed of 9:1 CO2:CO mixture at 1.5 V and 809 °C produced a current density of −0.78 A cm−2 even without more complex 3D electrode | electrolyte geometries

Theory and design of quantum cascade lasers in (111) n-type Si/SiGe

Although most work towards the realization of group IV quantum cascade lasers (QCLs) has focused on valence band transitions, there are many desirable properties associated with the conduction band. We show that the commonly cited shortcomings of n-type Si/SiGe heterostructures can be overcome by moving to the (111) growth direction. Specifically, a large band offset and low effective mass are achievable and subband degeneracy is preserved. We predict net gain up to lattice temperatures of 90 K in a bound-to-continuum QCL with a double-metal waveguide, and show that a Ge interdiffusion length of at least 8 Å across interfaces is tolerable