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

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

Density matrix modelling of Ge/GeSi bound-to-continuum terahertz quantum cascade lasers

In addition to the mainstream III-V quantum cascade lasers (QCLs), Si-based QCLs have attracted considerable research interest in recent years, due to their significant potential advantages including a mature Si processing technology, prospect of integration with Si microelectronics, superior thermal performance to that of III–V devices and absence of optical absorption in the Reststrahlen band [1–3]. Amongst various proposed designs, (001) oriented n-type Ge/GeSi structures utilising L-valley intersubband transitions appear to be the most promising due to a small quantisation effective mass, and hence large optical matrix elements and practically feasible layer widths [4]. All previous simulations for group IV-based QCLs followed the rate equation approach, which is considered not to be accurate enough for predicting the performance of terahertz QCLs, due to its limitation in describing coherent transport [5, 6]. Therefore, a quantum-mechanics approach such as non-equilibrium Green’s function or density matrix is required. Although the former is more accurate, its complexity and computational burden make it difficult to be implemented as a simulation tool. In this work, a density matrix (DM) model for Ge/SiGe QCL simulation has been developed. The existing models have used a reduced set of basis states, leaving out some coherences, which was justified for the particular structures they were used for, but potentially limits their generality and accuracy. In this work, we present an extended DM model, which considers all basis states involved in transport between periods of a QCL. The simulator based on it is sufficiently general to be able to simulate a QCL with any number of states and tight-binding modules per period. This is useful for investigating various QCL structures without modifying the code. It also includes multiple scattering mechanisms existing in Si and Ge quantum wells [4], i.e. intravalley scattering due to interface roughness, alloy disorder, ionized impurities, electron-electron, electron-acoustic phonon and optical phonon interactions, and intervalley phonon scattering. Since the simulator is still quite fast, it was used, in conjunction with a semi-automated optimization algorithm, to improve the predicted performance of bound-to-continuum QCLs, and to compensate for the gain-reduction associated with diffuse Ge/GeSi interfaces

Density matrix modelling of Ge/GeSi quantum cascade terahertz lasers

The prospect of making silicon-based quantum cascade lasers (QCLs) has attracted considerable research interest in recent years, due to their significant potential advantages including a mature Si processing technology, the prospect of integration with Si microelectronics, and superior thermal performance to that of III–V devices. Amongst various proposed designs, with different material compositions and substrate orientations, (001)-oriented n-type Ge/GeSi structures utilising L-valley intersubband transitions appear to be the most promising due to a small quantisation effective mass, and hence large optical matrix elements, and practically realisable layer widths. While all the previous simulations for group IV-based QCLs used the rate equation model, this neglects the coherence effects and is of limited usefulness for predicting QCL performance, particularly in the terahertz range. In this work, a quantum-mechanics transport model for Ge/SiGe QCL simulation has been developed, using the density matrix (DM) approach. In contrast to the existing DM formulations which have been used to simulate III-V based QCLs, the present model accounts for the role of all the QCL states in coherent transport, or in optical transitions, or both. The simulator includes all the principal scattering mechanisms in Ge/SiGe heterostructures: intravalley scattering due to interface roughness, alloy disorder, ionized impurities, electron-acoustic phonon and optical phonon interactions, and intervalley phonon scattering. It was used in conjunction with a semi-automated optimization algorithm to identify heterostructure designs for bound-to-continuum Ge/GeSi QCLs, and to compensate for the gain-reduction associated with diffuse Ge/GeSi interfaces

Intersubband transitions in n-type group IV quantum cascade lasers

In a theoretical investigation of intersubband transport in SiGe based quantum cascade structures, we show that low effective mass and a large confining potential may be achieved with either (001) oriented Ge-rich or (111) orientated Si-rich structures. Using a self-consistent time-independent perturbation/rate equation approach, we predict net gain in both systems and compare their maximum operating temperatures

Crystal orientation and waveguide geometry effects in n-type Si/SiGe quantum cascade lasers

The quantum cascade laser (QCL) was first demonstrated in 1994 as a compact source of mid-infrared radiation, but remains restricted to III-V compound semiconductors. There are however, many potential advantages associated with Si/SiGe alloys, and electroluminescence has been demonstrated in (001) oriented p-type cascade structures. Mature Si processing technology may reduce costs and offer a route to photonic integrated circuits. The absence of polar LO-phonon interactions may also allow higher temperature operation. The ∆ valleys in the conduction band of Si rich systems provide an alternative to p-type systems, and we have demonstrated theoretically that net gain is achievable. We determine the active region gain for an n-type bound-to-continuum QCL in both the (001) and (111) crystal orientations, using a rate equation/energy balance approach. We show that the (111) orientation offers larger usable band offsets and lower effective mass than the (001) orientation, and hence larger active region gain. We compare the maximum operating temperature and net gain for single and double metal waveguides of varying thicknesses and predict that the highest temperature operation is achievable with a double-metal waveguide and a 15 μm thick active region

Strain-engineering in Germanium membranes towards light sources on Silicon

Bi-axially strained Germanium (Ge) is an ideal material for Silicon (Si) compatible light sources, offering exciting applications in optical interconnect technology. By employing a novel suspended architecture with an optimum design on the curvature, we applied a biaxial tensile strain as large as 0.85% to the central region of the membrane