Laser cavity mirror imperfections and reflectivity: A time‐dependent numerical approach

While the cleaving process used for semiconductor Fabry–Pérot lasers produces atomically abrupt mirrors, there is considerable interest in mirrors defined by etching. Depending on the etching process employed, disorder of varying nature and degree results at the semiconductor–air interface. A theoretical approach capable of quantifying the impact of such disorder on the mirror reflectivity, to which laser performance is intimately connected, is presented. The theoretical technique is time‐dependent to facilitate visualization of the scattering process and is based on a locally one‐dimensional implicit‐finite‐difference approximation to the two‐dimensional scalar wave equation with variable coefficients. Mirror disorder is described in terms of a feature depth parameter and an in‐plane correlation length. The reflectivity falls off exponentially with disorder yet is found to remain close to its unperturbed value for the disorder scale attainable with the state‐of‐the‐art etching technology. © 1995 American Institute of Physics.  Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70593/2/APPLAB-66-3-288-1.pd

Effect of spectral broadening and electron‐hole scattering on carrier relaxation in GaAs quantum dots

Luminescence efficiency in quantum dots has been a matter of some controversy recently. Theoretically, poor efficiency has been predicted owing to the phonon bottleneck in carrier relaxation, while slightly enhanced luminescence has been reported in several experiments. The approach of this letter differs from previous theoretical work in that the scattering rates are computed self‐consistently accounting for the spectral broadening of the electronic spectra due to a finite energy level lifetime. Scattering of electrons and holes confined in the dot is found to be responsible for breaking the phonon bottleneck in electron relaxation reducing the relaxation time from several ns to several hundred ps. Results of a Monte Carlo simulation also including confined and interface polar optical phonon and acoustic phonon scattering for a range of quantum dot dimensions and temperatures are presented. These results may provide an explanation of the absence of a significant reduction in quantum dot luminescence compared with that from quantum wells.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71211/2/APPLAB-64-2-232-1.pd

A self‐consistent approach to spectral hole burning in quantum wire lasers

In a semiconductor laser above threshold, carriers are extracted at the lasing energy at a high rate due to stimulated emission and are injected at higher energies. This creates a ‘‘hole burning’’ phenomenon resulting in gain compression. This effect is studied in a quantum wire laser by solving the Boltzmann equation with sink and source terms by a novel Monte Carlo technique. The results for various values of the characteristic injection times are given. A formalism is also proposed for the fully self‐consistent determination of the laser operating parameters from the rate equations with the inclusion of nonlinear gain effects by substituting the correct form of the distribution function in presence of hole burning into the standard expressions for the laser material gain. The nonlinear gain effect is then described completely starting from the wire band structure and scattering rates. The generality of the proposed technique and its possible extensions and applications to the problem of nonlinear gain in quantum‐well lasers are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70724/2/JAPIAU-74-10-6451-1.pd

Dynamic instabilities in the power spectrum of deeply modulated semiconductor lasers

Semiconductor lasers under large‐signal direct modulation by a square waveform are found to exhibit a transition from a power spectrum characterized by a fundamental frequency and FM sidebands to a continuous spectrum with a catastrophically broadened linewidth of the order of several GHz. The interesting feature of the phenomenon is that the photon output remains periodic apart from noise‐induced fluctuations, and the broadening of the power spectrum is attributed to the sensitivity of the phase of the optical field to a large difference in the relaxation oscillation frequencies in the on and off states as well as the coupling between motions at the intrinsic resonance frequency of the system and the externally‐imposed modulation frequency. It is shown that under deep modulation by a periodic injection current, the optical phase becomes aperiodic generating a wide range of new frequencies in the power spectrum. It is also demonstrated that by confining the excursions of the injection current to the region of almost‐linear optical response, linewidth broadening may be avoided. Quantitative criteria for determining the boundary of the broadened‐linewidth region are presented for several modulation frequencies.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70720/2/JAPIAU-76-7-4003-1.pd

Theoretical optimization of quantum wire array lasers for low threshold current density and high modulation frequency

We show that as one decreases the cross‐sectional area of quantum wire lasers, the threshold current decreases, but the carrier relaxation time increases. Since the electron relaxation time sets the upper limit on the modulation frequency, there is a tradeoff between speed and efficiency in quantum wire lasers. We derive the optimal wire cross‐sectional area for a one‐dimensional array of quantum wire lasers based on a balance between an acceptably high maximum modulation frequency and a desirably low threshold current density. We find that for a relaxation time of 60 ps, the quantum wire of 150×150 Å cross section has the lowest threshold current density of 560 A/cm2. If high‐speed operation is not needed, the optimal choice for the quantum wire cross‐sectional area is 100×50 Å with the threshold current density of 420 A/cm2. For optimized quantum wells with the same cavity losses, the threshold current density is ≊620 A/cm2. We also present the results for the threshold current density and the relaxation time that allow one to find the optimal quantum wire structure weighing the speed and efficiency considerations in accordance with their relative importance.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70288/2/APPLAB-63-15-2024-1.pd

Spatial and spectral characteristics of spontaneous emission from semiconductor quantum wells in microscopic cylindrical cavities

The spontaneous emission rate from an In0.2Ga0.8As quantum well in a cylindrical dielectric cavity with submicron radii and without mirrors in the emission plane is calculated based on a rigorous description of the cavity modes and their interaction with the 2D electronic system. The rate is suppressed for radii much less than the peak optical wavelength (rcav≪λ/n), enhanced by up to a factor of ≊8 for rcav≊λ/n, and remains similar to its value in the absence of a cavity for rcav≫λ/n. The emitted light produces a highly collimated vertical beam in the intermediate region with the majority of photons emitted into the guided cavity modes, and its spatial distribution broadens dramatically in the smallest structures. The global spectral width of spontaneous emission in cavities that can presently be fabricated is largely unaffected by the introduction of lateral dielectric boundaries. © 1995 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70655/2/APPLAB-67-26-3865-1.pd

Growth and properties of ferromagnetic In(1-x)Mn(x)Sb alloys

We discuss a new narrow-gap ferromagnetic (FM) semiconductor alloy, In(1-x)Mn(x)Sb, and its growth by low-temperature molecular-beam epitaxy. The magnetic properties were investigated by direct magnetization measurements, electrical transport, magnetic circular dichroism, and the magneto-optical Kerr effect. These data clearly indicate that In(1-x)Mn(x)Sb possesses all the attributes of a system with carrier-mediated FM interactions, including well-defined hysteresis loops, a cusp in the temperature dependence of the resistivity, strong negative magnetoresistance, and a large anomalous Hall effect. The Curie temperatures in samples investigated thus far range up to 8.5 K, which are consistent with a mean-field-theory simulation of the carrier-induced ferromagnetism based on the 8-band effective band-orbital method.Comment: Invited talk at 11th International Conference on Narrow Gap Semiconductors, Buffalo, New York, U.S.A., June 16 - 20, 200

A general solution to the Schr\"odinger-Poission equation for charged hard wall: Application to potential profile of an AlN/GaN barrier structure

A general, system-independent formulation of the parabolic Schr\"odinger-Poisson equation is presented for a charged hard wall in the limit of complete screening by the ground state. It is solved numerically using iteration and asymptotic-boundary conditions. The solution gives a simple relation between the band bending and charge density at an interface. I further develop approximative analytical forms for the potential and wave function, based on properties of the exact solution. Specific tests of the validity of the assumptions leading to the general solution are made. The assumption of complete screening by the ground state is found be a limitation; however, the general solution still provides a fair approximate account of the potential when the bulk is doped. The general solution is further used in a simple model for the potential profile of an AlN/GaN barrier, and gives an approximation which compares well with the solution of the full Schr\"odinger-Poisson equation

Carrier relaxation in quantum wires: consequences for quantum wire laser performance

Quantum wire lasers are expected to require very low threshold currents owing to the nature of the 1D density of states which develops a sharp peak at the band edge and ensures superior laser characteristics. However, carrier relaxation processes in quasi-1D structures may be much slower than in bulk material owing to reduction in the momentum space. For very long relaxation times, these equilibrium processes are expected to limit the maximum modulation frequency of the quantum wire lasers. We perform a Monte Carlo simulation of electron relaxation in quantum wires with the inclusion of the electron-bulklike polar optical and acoustic phonon, electron-electron and electron-hole interactions as well as Thomas-Fermi screening. We find that for a carrier density of 1018 cm-3 the electron relaxation time ranges from 120 ps for the 100 AA*100 AA wire to 30 ps for the 200 AA*200 AA wire. Since the threshold current in a quantum wire laser increases with the wire cross section, within the limits of our relaxation model, this indicates possible existence of a trade-off between speed and efficiency in a quantum wire laser. We also analyse the effects of carrier relaxation on gain compression in quantum wire lasers by solving the Boltzmann equation using a novel Monte Carlo technique. A spectral hole forms in the carrier distribution at high injected currents with the resulting decrease in the slope of the light-current characteristic. The effect of a non-fermi-Dirac distribution of electrons is found to result in a suppression of the peak gain as compared with the peak gain calculated using the equilibrium distribution.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/48931/2/ss940ec9.pd