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 \eta_int that holds true for QD, QWR, and QW lasers. This expression directly relates the power and threshold characteristics. The key parameter, controlling \eta_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^2). Output powers in excess of 10 W at \eta_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.
Different approaches to the design of a genuinely temperature-insensitive quantum dot (QD) laser are proposed. Suppression of the parasitic recombination outside the QDs, which is the dominant source of the temperature dependence of the threshold current in the conventional design of a QD laser, is accomplished either by tunneling injection of carriers into the QDs or by band-gap engineering. Elimination of this recombination channel alone enhances the characteristic temperatures T_0 above 1000 K. Remaining sources of temperature dependence (recombination from higher QD levels, inhomogeneous line broadening, and violation of charge neutrality in QDs) are studied. Tunnelinginjection structures are shown to offer an additional advantage of suppressed e.ects of inhomogeneous broadening and neutrality violation.
We describe a mechanism of nonlinearity of the light-current characteristic common to heterostructure lasers with a reduced-dimensionality active region. It arises from (i) noninstantaneous carrier capture into the active region and (ii) nonlinear (in the carrier density) recombination rate outside the active region. Because of (i), the carrier density outside the active region rises with injection current above threshold, and because of (ii), 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 that holds true for quantum well, quantum wire, and quantum dot lasers.
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.
We propose a genuinely temperature-insensitive quantum dot (QD)
laser. Our approach is based on direct injection of carriers into
the QDs, resulting in a strong depletion of minority carriers in
the regions outside the QDs. Recombination in these regions,
which is the dominant source of the temperature dependence, is
thereby suppressed, raising the characteristic temperature T_0
above 1500 K. Still further enhancement of T_0 results from the
resonant nature of tunneling injection, which reduces the
inhomogeneous line broadening by selectively cutting off the
M.V. Maximov, L.V. Asryan, Yu.M. Shernyakov, A.F. Tsatsul'nikov, I.N. Kaiander, V.V. Nikolaev, A.R. Kovsh, S.S. Mikhrin, V.M. Ustinov, A.E. Zhukov, Zh.I. Alferov, N.N. Ledenstov, and D. Bimberg. "Gain and threshold characteristics of long wavelength lasers based on InAs/GaAs quantum dots formed by activated alloy phase separation". IEEE J. Quantum Electron., vol. 37, no. 5, pp. 676-683, May 2001.
Experimental and theoretical study was made of injection lasers based on InAs/GaAs quantum dots (QDs) formed by the activated alloy phase separation and emitting at about 1.3 mkm. Electoluminescence and gain spectra were investigated. The maximum modal gain is measured experimentally using two different techniques. Threshold current densities as low as 22 A/cm^2 per QD sheet were achieved. A step-like switch from ground- to excited-state transition lasing was observed with an increasing cavity loss. The characteristic temperatures for a sample with four cleaved sides and a 2-mm long stripe device at 300 K were 140 and 83 K, respectively. Single lateral-mode continuous-wave (CW) operation with the maximum output power of 210 mW was realized. Threshold characteristics of a laser were simulated taking into account radiative recombination in QDs, the wetting layer, and the optical confinement layer. The dependence of the threshold current density on the cavity length was shown to be extremely sensitive to the QD-array parameters determining the maximum gain for ground- and excited-state transitions and to the waveguide design. Our analysis reveals that nonradiative recombination channels may play an important role in the laser operation.
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.
Carrier photoexcitation from levels in quantum dots to continuous-spectrum states during lasing is analyzed theoretically. The simplest approach is used to provide upper estimates of the absorption coefficient and the photoexcitation cross section. Light absorption in carrier photoexcitation is shown to be essential for quantum dot laser operation only at very low total losses, e.g., in the case of long cavities.
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 multimode generation threshold in quantum-dot (QD) lasers is calculated as a function of the parameters of structure and temperature. Thermally excited escapes of carriers away from QDs are shown to control the multimode generation threshold. 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 the lasing is possible to attain, are shown to exist. Concurrent with the decrease of threshold current, the reduction of multimode generation threshold is shown to occur with decrease of temperature.
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 recombinati on 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 QD's. 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 QD's and the optimum thickness of the OCL, minimizing the threshold current density, are obtained. The characteristic temperature of QD laser T/sub 0/ is calculated for the first time considering carrier recombination in the OCL (barrier regions) and violation of the charge neutralit y in QDs. The inclusion of violation of the charge neutrality is shown to be critical for the correct calculation of T/sub 0/. The characteristic temperature is shown to fall off profoundly with increasing temperature. A drastic decrease in T/sub 0/ is shown to occur in passing from temperature conditions wherein the threshold current density is controlled by radiative recombination in QD's to temperature conditions wherein the threshold current density is controlled by radiative recombination i n the OCL. The dependences of T/sub 0/ on the root mean square of relative QD size fluctuations, total losses, and surface density of QDs are obtained
A theory of the gain and threshold current of a semiconductor quantum dot (QD) laser has been developed which takes account of the line broadening caused by fluctuations in QD size. Expressions for the threshold current versus the surface density of QDs, QD size dispersion and total losses have been obtained in explicit form. Optimization of the structure has been carried out, aimed at minimizing the threshold current density. The characteristic temperature of QD laser has been calculated considering carrier recombination in the optical confinement layer and violation of the charge neutrality in QDs.
The characteristic temperature of a quantum dot laser. T/sub 0/, has been calculated for the first time considering carrier recombination in the optical confinement layer and violation of the charge neutrality in QDs. T/sub 0/ is shown to fall off pr ofoundly with increasing temperature, which is in line with the available experimental results
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 acr oss 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 occupa ncies 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 vol tage 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
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 tog ether 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 a nd 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 func tions 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 laser