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

Self-consistent energy balance simulations of hole dynamics in SiGe/Si THz quantum cascade structures

Analysis of hole transport in cascaded p-Si/SiGe quantum well structures is performed using self-consistent rate equations simulations. The hole subband structure is calculated using the 6×6 k·p model, and then used to find carrier relaxation rates due to the alloy disorder, acoustic, and optical phonon scattering, as well as hole-hole scattering. The simulation accounts for the in-plane k-space anisotropy of both the hole subband structure and the scattering rates. Results are presented for prototype THz Si/SiGe quantum cascade structures. © 2004 American Institute of Physic

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

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

Stark ladders as tunable far-infrared emitters

A superlattice of GaAs/Ga(1 – x)Al(x)As quantum wells forms a Stark ladder under the influence of a perpendicular electric field. A two level incoherent emitter system, formed by radiative intersubband transitions between adjacent wells, is investigated as a tunable far-infrared radiation source. Intersubband transition rates are calculated at 4, 77, and 300 K for applied fields from 0 to 40 kV cm(–1). It is shown that the quantum efficiency of the radiative emission reaches a maximum at low temperatures for a field of 32 kV cm(–1). Under these conditions the emission wavelength is 38 µm with an estimated power output of 1.1 mW. © 1998 American Institute of Physics

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

Intersubband carrier scattering in n- and p-Si/SiGe quantum wells with diffuse interfaces

Scattering rate calculations in two-dimensional Si/Si1−xGex systems have typically been restricted to rectangular Ge profiles at interfaces between layers. Real interfaces however, may exhibit diffuse Ge profiles either by design or as a limitation of the growth process. It is shown here that alloy disorder scattering dramatically increases with Ge interdiffusion in (100) and (111) n-type quantum wells, but remains almost constant in (100) p-type heterostructures. It is also shown that smoothing of the confining potential leads to large changes in subband energies and scattering rates and a method is presented for calculating growth process tolerances

Further extensions to rectangular dielectric waveguide technique for dielectric measurements

This paper describes a method to obtain the dielectric constant of materials using the rectangular dielectric waveguide technique in the WR-22 frequency band. By applying the solution of the wave equation, the actual dielectric constant for samples of small transverse dimensions can be directly recovered from the measured effective dielectric constant by a numerical technique. The method is very quick and simple and provides sufficient accuracy for most practical purpose

Towards automated design of quantum cascade lasers

We present an advanced technique for the design and optimization of GaAs/AlGaAs quantum cascade laser structures. It is based on the implementation of the simulated annealing algorithm with the purpose of determining a set of design parameters that satisfy predefined conditions, leading to an enhancement of the device output characteristics. Two important design aspects have been addressed: improved thermal behavior, achieved by the use of higher conduction band offset materials, and a more efficient extraction mechanism, realized via a ladder of three lower laser states, with subsequent pairs separated by the optical phonon energy. A detailed analysis of performance of the obtained structures is carried out within a full self-consistent rate equations model of the carrier dynamics. The latter uses wave functions calculated by the transfer matrix method, and evaluates all relevant carrier–phonon and carrier–carrier scattering rates from each quantized state to all others within the same and neighboring periods of the cascade. These values are then used to form a set of rate equations for the carrier density in each state, enabling further calculation of the current density and gain as a function of the applied field and temperature. This paper addresses the application of the described procedure to the design of lambda~9 µm GaAs-based mid-infrared quantum cascade lasers and presents the output characteristics of some of the designed optimized structures. © 2005 American Institute of Physic

Population inversion in optically pumped asymmetric quantum well terahertz lasers

Intersubband carrier lifetimes and population ratios are calculated for three- and four-level optically pumped terahertz laser structures. Laser operation is based on intersubband transitions between the conduction band states of asymmetric GaAs-Ga(1 – x)Al(x)As quantum wells. It is shown that the carrier lifetimes in three-level systems fulfill the necessary conditions for stimulated emission only at temperatures below 200 K. The addition of a fourth level, however, enables fast depopulation of the lower laser level by resonant longitudinal optical phonon emission and thus offers potential for room temperature laser operation. © 1997 American Institute of Physics