In this paper we report on carrier lifetime measurements performed on 1.3 μm p-doped InAs quantum-dot lasers. The carrier lifetimes were determined by fitting the measured sub-threshold optical modulation response to a single pole response function, and then correcting this time constant for the diode junction capacitance to obtain the carrier lifetime. The sub-threshold frequency response curves did indeed show a single pole behavior at all the bias currents and, as expected, the extracted carrier lifetimes monotonically decrease with increasing bias currents. The differential carrier lifetime versus bias current data was then fitted, using a simple single carrier level rate equation analysis, to determine the recombination coefficients. Using this simplified analysis, the values of the recombination coefficients are found to be: A = 1.0 x 107 /s, B = 2.5 x 10-11 cm3/s, and C = 1.1 x 10-29 cm6/s at room temperature. Since, the carriers are distributed among the dots in a complicated manner that depends on bias, the lifetimes and recombination coefficients extracted using the single carrier level analysis are the effective or average values. Thus we have also built a multi-level rate equation model including the capture and escape times between various QD and wetting layer states. The multi-level rate equation model yields intrinsic recombination coefficients of AQD = 5.5 x 107 /s, BQD = 6.5 x 10-11 cm3/s, CQD = 5.6 x 10-29 cm6/s. Regardless of the model used the dominant contribution to the threshold current is found to be Auger recombination which accounts for approximately 80 % of the threshold current in our 1.3 μm p-doped QD lasers.
Carrier lifetime measurements are a powerful tool to understand and quantify the recombination mechanisms in semiconductor lasers. In this work we report the results of carrier lifetime measurements performed on 1.3 μm p-doped InAs Quantum-Dot lasers at room temperature using the small-signal modulation technique. The carrier lifetime at a particular bias current is determined by fitting the measured optical frequency response curves to the calculated response derived from sub-threshold carrier and photon rate equations. Calculated optical response curves are dominated by a single pole regardless of whether a single or multiple carrier level rate equation analysis is used. We also measure a single pole optical response, throughout the entire range of bias currents, thus allowing us to extract the differential carrier lifetime. The recombination coefficients are extracted by simultaneously fitting the variation of differential carrier lifetime with bias current to equations relating the current and carrier lifetime to the recombination coefficients and carrier density. Specifically we find a cubic (or Auger) recombination coefficient of 1.2 x 10-29 cm6/s and 5.6 x 10-29 cm6/s in the single and multi carrier level rate equations respectively, while the bimolecular (radiative) coefficients are 1.8 x 10-11 cm6/s and 6.5 x 10-11 cm6/s, and the monomolecular (defect) coefficients are 2.9x107 /s and 5.5x107 /s. Regardless of the analysis used we find that the vast majority, approximately 80%, of the current at threshold is due to the cubic recombination process which is traditionally assumed to be Auger recombination.
In this work we study the role of free carriers and excitons on the characteristics of 1.3 μm InAs/InGaAs quantum dot lasers. The study is carried out theoretically by building a mathematical model to calculate the threshold current in the laser and the charateristic temperature, T0. In order to determine the role of free carrier and excitons on the laser characteristics the model allows for different carrier distribution assumptions to be used, and we look at three cases; all free carriers, all excitons, and both free carriers and excitons in the dots. Our model results show that if we allow either free carriers or excitons to exist but not both, the calculated threshold current and T0 do not match with the experimental values. Thus we conclude that both free and bound carriers must exist and develop a method for modeling this case. We use a modified form of the Saha equation to calculate the ratio of free carriers to excitons and modify the material gain to account for this ratio. This model results in a threshold current density of approximately 39 A/cm2 and a T0 of 83 K, both of which are in excellent agreement with experimental results.
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