Robert A. Suris

Inhomogeneous line broadening and the threshold current density of a semiconductor quantum dot laser

Theoretical analysis of the gain and threshold current of a semiconductor quantum dot (QD) laser is given which takes account of the line broadening caused by fluctuations in quantum dot sizes. The following processes are taken into consideration together with the main process of radiative recombination of carriers in QDs: band-to-band radiative recombination of carriers in the waveguide region, carrier capture into QDs and thermally excited escape from QDs, photoexcitation of carriers from QDs to continuous-spectrum states. For an arbitrary QD size distribution, expressions for the threshold current density as a function of the root mean square of relative QD size fluctuations, total losses in the waveguide region, surface density of QDs and thickness of the waveguide region have been obtained in an explicit form. The minimum threshold current density and optimum parameters of the structure (surface density of QDs and thickness of the waveguide region) are calculated as universal functions of the main dimensionless parameter of the theory developed. This parameter is the ratio of the stimulated transition rate in QDs at the lasing threshold to the spontaneous transition rate in the waveguide region at the transparency threshold. Theoretical estimations presented in the paper confirm the possibility of a significant reduction of the threshold currents of QD lasers as compared with the conventional quantum well lasers.

Temperature dependence of the threshold current density of a quantum dot laser

Detailed theoretical analysis of the temperature dependence of threshold current density of a semiconductor quantum dot (QD) laser is given. Temperature dependences of the threshold current density components associated with the radiative recombination in QDs and in the optical confinement layer (OCL) are calculated. Violation of the charge neutrality in QDs is shown to give rise to the slight temperature dependence of the current density component associated with the recombination in QDs. The temperature is calculated (as a function of the parameters of the structure) at which the components of threshold current density become equal to each other. Temperature dependences of the optimum surface density of QDs and the optimum thickness of the OCL, minimizing the threshold current density, are obtained. The characteristic temperature of QD laser T/sub o/ is calculated for the first time considering carrier recombination in the OCL (barrier regions) and violation of the charge neutrality in QDs. The inclusion of violation of the charge neutrality is shown to be critical for the correct calculation of T/sub o/. The characteristic temperature is shown to fall off profoundly with increasing temperature. A drastic decrease in T/sub o/ is shown to occur in passing from temperature conditions wherein the threshold current density is controlled by radiative recombination in QDs to temperature conditions wherein the threshold current density is controlled by radiative recombination in the OCL. The dependences of T/sub o/ on the root mean square of relative QD size fluctuations, total losses, and surface density of QDs are obtained.

Charge neutrality violation in quantum-dot lasers

Theory of quantum-dot (QD) lasers is augmented to include, in a self-consistent manner, the QD-layer charge. The electron- and hole-level occupancies in QDs are obtained through the solution of the problem for the electrostatic-field distribution across the junction. They are shown to differ from each other. As a result, the local neutrality is broken down in each QD, i.e., the QD layer is charged. The key dimensionless parameters controlling the difference of the hole- and electron-level occupancies are revealed. The detailed analysis of the gain and spontaneous radiative recombination current density is given, having regard to the fact of violation of the charge neutrality in QDs. The gain-current density dependence is calculated, The voltage dependences of the electron- and hole-level occupancies, gain, and current density are obtained. Particular emphasis is given to the transparency and lasing threshold characteristics. Optimization of the QD-laser structure is carried out. The optimum surface density of QDs, minimizing the threshold current density, is shown to be distinctly higher than that calculated without regard for the lack of the charge neutrality in QDs.

Threshold characteristics of InGaAsP/InP multiple quantum well lasers

A theoretical analysis and computer simulation of the threshold current density jth and characteristic temperature T0 of multiple quantum well lasers (MQWLs) are presented. Together with the spontaneous radiative recombination, the Auger recombination and the lateral diffusive leakage of carriers from the active region are included into the model. A first-principle calculation of the Auger recombination current is performed. It is shown that the lateral diffusive leakage current is controlled by the radiative and Auger currents. When calculating the carrier densities, the electrons in the barrier regions are properly taken into account. Redistribution of electrons over the active region is shown to increase the threshold current considerably. The dependences of jth and T0 on temperature, number of QWs, cavity length and lateral size are discussed in detail. The effect of lattice and carrier heating on jth and T0 is investigated and shown to be essential at high temperature.

Maximum modal gain of a self-assembled InAs/GaAs quantum-dot laser

Gain and threshold current of a self-assembled InAs/GaAs quantum-dot (QD) laser are simulated. A small overlap integral of the electron and hole wave functions in pyramidal QDs is shown to be a possible reason for the low single-layer modal gain, which limits lasing via the ground-state transition at short (under a millimeter) cavity lengths.

Internal efficiency of semiconductor lasers with a quantum-confined active region

We discuss in detail a new mechanism of nonlinearity of the light-current characteristic (LCC) in heterostructure lasers with reduced-dimensionality active regions, such as quantum wells (QWs), quantum wires (QWRs), and quantum dots (QDs). It arises from: 1) noninstantaneous carrier capture into the quantum-confined active region and 2) nonlinear (in the carrier density) recombination rate outside the active region. Because of 1), the carrier density outside the active region rises with injection current, even above threshold, and because of 2), the useful fraction of current (that ends up as output light) decreases. We derive a universal closed-form expression for the internal differential quantum efficiency /spl eta//sub int/ that holds true for QD, QWR, and QW lasers. This expression directly relates the power and threshold characteristics. The key parameter, controlling /spl eta//sub int/ and limiting both the output power and the LCC linearity, is the ratio of the threshold values of the recombination current outside the active region to the carrier capture current into the active region. Analysis of the LCC shape is shown to provide a method for revealing the dominant recombination channel outside the active region. A critical dependence of the power characteristics on the laser structure parameters is revealed. While the new mechanism and our formal expressions describing it are universal, we illustrate it by detailed exemplary calculations specific to QD lasers. These calculations suggest a clear path for improvement of their power characteristics. In properly optimized QD lasers, the LCC is linear and the internal quantum efficiency is close to unity up to very high injection-current densities (15 kA/cm/sup 2/). Output powers in excess of 10 W at /spl eta//sub int/ higher than 95% are shown to be attainable in broad-area devices. Our results indicate that QD lasers may possess an advantage for high-power applications.

Nonlinear effects in microwave photoconductivity of two-dimensional electron systems

We present a model for microwave photoconductivity of two-dimensional electron systems in a magnetic field which describes the effects of strong microwave and steady-state electric fields. Using this model, we derive an analytical formula for the photoconductivity associated with photon- and multi-photon-assisted impurity scattering as a function of the frequency and power of microwave radiation. According to the developed model, the microwave conductivity is an oscillatory function of the frequency of microwave radiation and the cyclotron frequency which turns zero at the cyclotron resonance and its harmonics. It exhibits maxima and minima (with absolute negative conductivity) at the microwave frequencies somewhat different from the resonant frequencies. The calculated power dependence of the amplitude of the microwave photoconductivity oscillations exhibits pronounced sublinear behavior similar to a logarithmic function. The height of the microwave photoconductivity maxima and the depth of its minima are nonmonotonic functions of the electric field. It is pointed to the possibility of a strong widening of the maxima and minima due to a strong sensitivity of their parameters on the electric field and the presence of strong long-range electric-field fluctuations. The obtained dependences are consistent with the results of the experimental observations.We present a model for microwave photoconductivity of two-dimensional electron systems in a magnetic field which describes the effects of strong microwave and steady-state electric fields. Using this model, we derive an analytical formula for the photoconductivity associated with photon- and multi-photon-assisted impurity scattering as a function of the frequency and power of microwave radiation. According to the developed model, the microwave conductivity is an oscillatory function of the frequency of microwave radiation and the cyclotron frequency which becomes zero at the cyclotron resonance and its harmonics. It exhibits maxima and minima (with absolute negative conductivity) at microwave frequencies somewhat different from the resonant frequencies. The calculated power dependence of the amplitude of the microwave photoconductivity oscillations exhibits pronounced sublinear behaviour similar to a logarithmic function. The height of the microwave photoconductivity maxima and the depth of its minima are nonmonotonic functions of the electric field. The possibility of a strong widening of the maxima and minima due to a strong sensitivity of their parameters on the electric field and the presence of strong long-range electric-field fluctuations is pointed to. The obtained dependences are consistent with the results of the experimental observations.

Effect of excited-state transitions on the threshold characteristics of a quantum dot laser

The general relationship between the gain and spontaneous emission spectra of a quantum dot (QD) laser is shown to hold for an arbitrary number of radiative transitions and an arbitrary QD-size distribution. The effect of microscopic parameters (the degeneracy factor and the overlap integral for a transition) on the gain is discussed. We calculate the threshold current density and lasing wavelength as a function of losses. The conditions for a smooth or step-like change in the lasing wavelength are described. We have simulated the threshold characteristics of a laser based on self-assembled pyramidal InAs QDs in the GaAs matrix and obtained; a small overlap integral for transitions in the QDs and a large spontaneous radiative lifetime. These are shown to be a possible reason for the low single-layer modal gain, which limits lasing via the ground-state transition for short (several hundreds of micrometers) cavity lengths.

Longitudinal spatial hole burning in a quantum-dot laser

Detailed theoretical analysis of longitudinal spatial hole burning in quantum-dot (QD) lasers is given. Unlike conventional semiconductor lasers, escape of thermally excited carriers from QDs, rather than diffusion, is shown to control the smoothing-out of the spatially nonuniform population inversion and multimode generation in QD lasers. The multimode generation threshold is calculated as a function of structure parameters (surface density of QDs, QD size dispersion, and cavity length) and temperature. A decrease in the QD size dispersion is shown to increase considerably the relative multimode generation threshold. The maximum tolerable QD size dispersion and the minimum tolerable cavity length, at which lasing is possible to attain, are shown to exist. Concurrent with the increase of threshold current, an increase of the multimode generation threshold is shown to occur with a rise in temperature. Ways to optimize the QD laser, aimed at maximizing the multimode generation threshold, are outlined.

The role of surface diffusion of adatoms in the formation of nanowire crystals

A model of the formation of nanowire crystals on surfaces activated by droplets of the catalyst of growth is developed. In the model, the diffusion of adatoms from the surface of the substrate to the lateral surface of the crystals is taken into account. The exact solution of the diffusion problem for the flow of adatoms from the surface to the nanowire crystals is obtained, and the particular cases of the solution for the short and long diffusion lengths of adatoms, λs, are analyzed. A general expression for the length of the nanowire crystals, L, in relation to their radius R and to the conditions of growth is derived. The expression is applicable to a large variety of technologies of growth. The theoretical results are compared with the experimental dependences L(R) in the range of R = 20–250 nm for GaAs nanowire crystals grown by molecular-beam epitaxy on the GaAs (111) V Ga surface activated by Au. It is shown that, in some range of the parameters, the dependence L(R) follows the function 1/R2ln(λs/R), which is radically different from the classical diffusion dependence 1/R.