Conventional diode lasers suffer from electron-hole recombination outside of their active region [primarily in the optical confinement layer (OCL) but also in the wetting layer in the case of quantum dot (QD) lasers]. This parasitic recombination negatively impacts the laser’s operating characteristics by raising the threshold current, making it more temperaturesensitive (decreasing the characteristic temperature), and leading to sublinear light-current characteristics. One proposed solution to this problem is the addition of asymmetric barrier layers (ABLs) in the OCL – one on each side of the active region. Ideally, if the ABLs are properly tuned, parasitic recombination outside of the active region (i.e., in the entire OCL) should be entirely suppressed. However, due to material constraints, it may be desirable to first manufacture a laser with only a single ABL suppressing parasitic recombination only on one side of the OCL. Here we study the effect of a single ABL on the steady-state operation of QD lasers. Our theoretical model is based on the set of rate equations for charge carriers in the multilayer structure and photons. We show that, despite the limited improvement to output optical power, the addition of a single ABL significantly improves the temperature stability of the laser – its characteristic temperature is much higher than that of the conventional QD laser. Our study thus justifies the concept of using even a single ABL in injections lasers for improving their operating characteristics.
The parasitic electron-hole recombination outside of a quantum-confined active region still presents a challenge in conventional injection lasers. The use of asymmetric barrier layers (ABLs) (one on each side of the active region) should efficiently suppress this recombination. However, even in lasers with ABLs, excited states may be present in the active region in addition to the ground state. Excited states may strongly affect delivery of charge carriers to the lasing ground state. In this work, dynamic properties of quantum dot (QD) lasers with ABLs are studied in the presence of excited states in QDs. The situation is considered when the carrier capture into the lasing ground state in QDs is excited-state-mediated. It is shown that the modulation bandwidth of the ABL QD laser can be considerably impacted by excited-to-ground state relaxation delay in QDs. Hence a strict control of the intradot relaxation time will be required to enhance the modulation bandwidth in ABL QD lasers.
The small-signal dynamic response of quantum dot (QD) lasers with asymmetric barrier layers (ABLs) is studied. The modulation bandwidth of this novel type of laser is shown to have a maximum as a function of the dc component of the pump current and parameters of the structure. This provides a clear path for optimizing the laser structure to enhance its bandwidth. The effect of non-instantaneous capture of electrons and holes into QDs on the modulation bandwidth is studied. The maximum bandwidth and the optimum dc injection current at which it is attained are calculated as functions of the capture cross-section. The optimum dc injection current is shown to be considerably lower in ABL QD lasers as compared to conventional QD lasers, i.e., the maximum bandwidth is easier to attain in ABL QD lasers.
The temperature behavior of operating characteristics in semiconductor lasers with a quantum-confined active region is studied with a proper account for (i) non-instantaneous capture of charge carriers from the waveguide region into the active region and (ii) internal optical loss that depends on the carrier densities. Because of (i), the carrier densities are not pinned in the lasing mode, i.e., they are functions of the injection current. In view of (ii) and as a result of pump-currentdependence of the carrier densities, so becomes the internal loss coefficient. This in turn leads to the roll-over of the light-current characteristic at high currents (i.e., decreasing optical power with increasing injection current) and, under certain conditions, appearance of the second branch in it. The laser characteristics are shown to transform qualitatively with varying temperature: they are conventional, i.e., consist of one branch, at low temperatures but they have two branches, i.e., are of a binary nature, at high temperatures. The two branches merge together at the maximum operating current beyond which the lasing quenches. In contrast to the first (conventional) lasing threshold, the threshold for emerging the second branch decreases with increasing temperature. The pump-current-dependence of the carrier densities and internal loss coefficient is also fascinating: these quantities decrease with increasing current in their second branches.
The light-current characteristic (LCC) of quantum dot (QD) lasers is studied in the presence of internal optical absorption loss, which varies with charge carrier density in the waveguide region. Depending on the parameters of the structure, the LCC is shown to be either one- or two-valued. In one-valued LCC, the output optical power increases with increasing injection current, approaches its maximum, rolls over on further increasing current, and finally goes to zero at the maximum operating current. The output power in the first branch of a two-valued LCC behaves similarly to that in a one-valued LCC with the only difference that it is non-zero at the maximum operating current, beyond which the lasing quenches. Besides, at a certain current (second threshold current) exceeding the threshold current for the first branch (first threshold current), the second branch emerges in the LCC. The output power in this branch increases monotonously with increasing current; at the maximum operating current (which is the same as that for the first branch), the two branches merge together. An analytical criterion is derived, which determines whether the LCC will be one- or two-valued. The following parameters enter into this criterion and hence control the shape of the LCC: cross-section of internal loss, maximum modal gain (which, in turn, is controlled by the QD-size dispersion), cross-section of carrier capture into QDs, thickness of the waveguide region, and spontaneous radiative recombination coefficient in that region. The transformation of the LCC shape (from one- to two-valued), which occurs via the variation of the above parameters, is discussed.
An analytical model for operating characteristics of a novel type of semiconductor lasers, quantum dot (QD) lasers with asymmetric barrier layers (ABLs), is discussed. In such lasers, the ABLs (one on each side of the active layer with QDs) should ideally keep the electron-injecting side of the structure completely devoid of holes and the hole-injecting side devoid of electrons thus eliminating the parasitic electron-hole recombination there. In actual structures, however, the ABLs will only partly fulfill this function; as a result, there will be a certain fraction of electrons on the hole-injecting side and holes on the electron-injecting side and, hence, the parasitic electron-hole recombination will still occur outside QDs in addition to the useful electron-hole recombination in QDs. In this work, the effect of non-ideality of ABLs on threshold and high-power characteristics of ABL QD lasers is theoretically studied. The extent, to which the laser operating characteristics are affected, is quantified by deriving and analyzing closed-form expressions for the threshold current density, characteristic temperature, internal differential quantum efficiency, and output optical power as functions of non-ideality of ABLs. Approaches for optimizing the ABL QD lasers performance are discussed.
To overcome the limitations placed on the operating characteristics of diode lasers by recombination outside their active region, two novel designs were proposed for them: one using double tunneling-injection (injection of both electrons and holes) into the active region, and the other using two asymmetric barrier layers (ABLs) flanking the active region. The barrier layers are asymmetric in that they have considerably different heights for the carriers of opposite signs. The ABL located on the electron- (hole-) injecting side of the structure provides a low barrier (ideally no barrier) for electrons (holes) [so that it does not prevent electrons (holes) from easily approaching the active region] and a high barrier for holes (electrons) [so that holes (electrons) injected from the opposite side of the structure do not overcome it]. The use of ABLs should thus ideally prevent the simultaneous existence of electrons and holes (and hence parasitic electron-hole recombination) outside the active region. In this work, we calculate the threshold and power characteristics of quantum dot lasers with ABLs. We show that quantum dot lasers with ABLs offer close-to-ideal performance: low threshold current density, very high characteristic temperature (virtually temperature-independent operation), close-to-unity internal differential quantum efficiency, and linear light-current characteristic.
Dynamic characteristics of double tunneling-injection (DTI) quantum dot (QD) lasers are studied. To reveal the potential of such lasers for high-speed direct modulation of their optical output by pump current, fast carrier injection into QDs and no carrier leakage from QDs are assumed. The small-signal analysis of rate equations is applied. The modulation bandwidth is calculated as a function of the dc component of the injection current density and parameters of the laser structure.
We show that the carrier capture from the optical confinement layer into quantum dots (QDs) can strongly limit the
modulation bandwidth ω-3 dB of a QD laser. Closed-form analytical expressions are obtained for ω-3 dB in the limiting cases of fast and slow capture. ω-3 dB is highest in the case of instantaneous capture into QDs, when the cross-section of carrier capture into a QD σn = ∞. With reducing σn, ω-3 dB decreases and becomes zero at a certain non-vanishing value σnmin. This σnmin presents the minimum tolerable capture cross-section for the lasing to occur at a given dc component j0 of the injection current density. The higher is j0, the smaller is σnmin and hence the direct modulation of the output power is possible at a slower capture. The use of multiple layers with QDs is shown to considerably improve the modulation response of the laser - the same ω-3 dB is obtained in a multi-layer structure at a much lower j0 than in a single-layer structure. At a plausible value of σn = 10-11 cm2, ω-3 dB as high as 19 GHz is attainable in a 5-QD-layer structure.
Effect of the wetting layer (WL) on the output power of a double tunneling-injection (DTI) quantum dot (QD) laser is
studied. Such a laser was proposed earlier to suppress bipolar population and hence electron-hole recombination outside
QDs. In the Stranski-Krastanow growth mode, QDs are formed on an initially grown WL. The WL is directly connected
to QDs by the processes of carrier capture and thermal escape. These processes are described in terms of the temporal
cross-sections of electron and hole capture from the WL into QDs. The electron and hole densities and parasitic electron-hole
recombination current density in the WL, and the output power of the device are calculated as functions of the
temporal cross-sections. These calculations provide the basis for optimization of a DTI QD laser with the WL aimed at
maximizing the output power. The larger the temporal cross-section of electron capture into QDs, the more efficient is
the electron capture from the WL into QDs, and hence the higher is the output power. The smaller the temporal crosssection
of hole capture into QDs, the less intensive is the hole thermal escape from QDs into the WL, the less intensive is
the recombination in the WL, and hence the higher is the output power.
Dynamic effects in a quantum dot (QD) laser are studied theoretically. The frequency and decay rate of relaxation
oscillations, and the modulation response are calculated as functions of injection current density, cavity length, and
parameters of the QD structure. The highest possible bandwidth is calculated and shown to increase with increasing
overlap integral between the electron and hole wave functions in a QD, number of QD-layers and surface density of QDs
in a layer, and with reducing QD-size dispersion.
Emission of higher-order modes caused by spatial hole burning in a quantum dot (QD) laser is studied. The critical
tolerable values of the structure parameters are discussed beyond which higher-order longitudinal modes can not
oscillate. The higher the mode order, the narrower the range of allowed QD-size scatter for lasing of the mode. The
higher the mode order, the denser the QD-ensemble and the longer the cavity should be for lasing of the mode. The
output powers of the lasing modes are calculated versus the injection-current density from the solution of the rate
equations.
Carrier-density-dependent internal optical loss sets an upper limit for operating temperatures and considerably reduces the characteristic temperature of a quantum dot (QD) laser. Such a loss also constrains the shallowest potential well depth and the smallest tolerable size of a QD at which the lasing can be attained. In a laser with a single layer of QDs, this loss can strongly limit the output power and cause a rollover of the light-current curve; it also imposes limitations on the conventional method of determining the internal quantum efficiency. Excited-state-mediated capture of carriers from the waveguide into the QD ground-state places a fundamental limitation on ground-state lasing - the output power saturates at high injection currents. The saturation power is controlled by the transition time between the excited- and ground-state in a QD. The longest, cut-off transition time exists, beyond which no ground-state lasing is possible. The maximum number of longitudinal modes that can oscillate in a QD laser increases with increasing surface density of QDs and remains limited (first increases and then decreases) with increasing scatter in the QD-size. In addition to the maximum tolerable scatter, there also exists the minimum scatter in the QD-size for each higher-order mode to start lasing.
The potential for high-power operation of a laser exploiting tunneling-injection of electrons and holes into quantum dots
(QDs) from two separate quantum wells (QWs) is studied. An extended theoretical model is developed to account for
out-tunneling leakage of carriers from QDs. Even in the presence of out-tunneling from QDs, the parasitic recombination
flux outside QDs is shown to remain restricted with increasing injection current; correspondingly, the LCC becomes
more and more linear and the slope efficiency closer to unity at high injection currents. The linearity is due to the fact
that the current paths connecting the opposite sides of the structure lie entirely within QDs - in view of the threedimensional
confinement in QDs, the out-tunneling fluxes of carriers from dots are limited.
Carrier-density-dependent internal optical loss sets an upper limit for operating temperatures and considerably reduces
the characteristic temperature of a quantum dot laser. Such internal loss also constrains the shallowest potential well
depth and the smallest tolerable size of a quantum dot at which the lasing can be attained. At the maximum operating
temperature or when any parameter of the structure is equal to its critical tolerable value, the characteristic temperature
drops to zero.
Excited-state-mediated capture of carriers from the waveguide into the lasing ground-state in quantum dots (QDs) is
studied. Such a two-step capture places a fundamental limitation on ground-state lasing - the output power saturates at
high injection currents. The saturation power is controlled by the transition time between the excited- and ground-state in
a QD. The longest, cut-off transition time exists, beyond which no ground-state lasing is possible.
Feasibility is discussed of the conventional method of determining internal loss coefficient and internal quantum efficiency from a measured plot of the reciprocal slope efficiency versus the cavity length L in semiconductor edge-emitting quantum dot (QD) lasers. The limitations are imposed by the cavity-length-dependence of internal loss and quantum efficiency themselves. The effect of internal loss is quantitatively analyzed, which originates from the dependence of internal loss on the carrier density, with the latter being L-dependent. In short cavities, a plot of the reciprocal slope efficiency versus the cavity length can significantly deviate from a straight line; particularly, the reciprocal slope efficiency increases with reducing the cavity length in short cavities. This plot asymptotically approaches an inclined line only in long cavities. Correspondingly, only infinitely-long-cavity (no mirror loss) values of the internal loss coefficient and the internal quantum efficiency can be extracted using the standard procedure. These latter differ significantly from those in short-cavity devices, thus strongly limiting the practicality of the procedure. For L longer than several hundred microns, the limitations are strong in a single-QD-layer laser and moderate in a multiple-QD-layer laser.
We develop a general approach to including the internal optical loss in the description of semiconductor lasers with a quantum-confined active region. We assume that the internal absorption loss coefficient is linear in the free-carrier density in the optical confinement layer and is characterized by two parameters, the constant component and the net cross-section for all absorption loss processes. We show that the free-carrier-density dependence of internal loss gives rise, in general, to the existence of a second lasing threshold above the conventional threshold. Above the second threshold, the light-current characteristic is two-valued up to a maximum current at which the lasing is quenched. We show that the presence of internal loss narrows considerably the region of tolerable structure parameters in which the lasing is attainable; for example, the minimum cavity length is significantly increased. Our approach is quite general but the numerical examples presented are specific for quantum dot (QD) lasers. Our calculations suggest that the internal loss is likely to be a major limiting factor to lasing in short-cavity QD structures.
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 bandgap engineering. Elimination of this recombination channel alone enhances the characteristic temperature T0 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. Tunneling injection structures are shown to offer an additional advantage of suppressed effects of inhomogeneous broadening and neutrality violation.
Theoretical study of threshold characteristics of a quantum dot (QD) laser in the presence of excited-state transitions is given. The effect of microscopic parameters (degeneracy factor and overlap integral for a transition) on the gain is discussed. An analytical equation for the gain spectrum is derived in an explicit form. Transformation of the gain spectrum with the injection current is analyzed. The threshold current density is calculated as a function of the total losses. The conditions for a smooth or step-like change in the lasing wavelength with the losses are formulated. Threshold characteristics of a laser based on self-assembled pyramidal InAs QDs in GaAs matrix are simulated. A small overlap integral for transitions in such QDs (and hence large spontaneous radiative lifetime) is shown to be a main possible reason for a low value of the maximum single-layer modal gain of the respective structure which is deficient to attain lasing at moderately short (several hundreds of micrometers) cavity lengths.
Detailed theoretical analysis of the temperature dependence of threshold current density of a semiconductor quantum dot (QD) laser, jth, is given. Temperature dependences of the components of jth 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 jth become equal to each other. Temperature dependences of the optimum surface density of QDs and the optimum thickness of the OCL, minimizing jth, are obtained. The characteristic temperature of QD laser, T0, is calculated 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 T0. The characteristic temperature is shown to fall off profoundly with increasing temperature. A drastic decrease in T0 is shown to occur in passing from temperature conditions wherein jth is controlled by radiative recombination in QDs to temperature conditions wherein jth is controlled by radiative recombination in the OCL. The dependences of T0 on the root mean square of relative QD size fluctuations, total losses and surface density of QDs are obtained.
Theoretical analysis of the gain and threshold current of a quantum dot (QD) laser is given taking into account the linewidth broadening caused by fluctuations in QD sizes. The following processes are taken into consideration together with the main process of the radiative recombination of carriers in QDs: the band-to-band radiative recombination of carriers in the waveguide region, carrier capture into QDs, and thermally excited escape from QDs. Expressions for the threshold current density depends on the root mean square of QD size relative fluctuations, surface density of QDs, thickness of the waveguide region, and total losses that have been obtained in an explicit form. The minimal threshold current density and optical values of the structure parameters are calculated as univeral functions of the main dimensionless parameter of the elaborated theory. This parameter is the ratio of the simulated transition rate in QDs to the spontaneous transition rate in the waveguide region. Theoretical estimations presented in the paper confirm the possibility of a significant reduction of the threshold currents of QD lasers as compared with conventional quantum well lasers.
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