IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 44, NO. 2, FEBRUARY 2008 175 Gain Studies on Quantum-Dot Lasers With Temperature-Stable Emission Wavelength Ralph Debusmann, Thomas W. Schlereth, Sven Gerhard, Wolfgang Kaiser, Sven Höfling, Member, IEEE, and Alfred Forchel, Member, IEEE Abstract—In this paper, a comparative study of the gain spectra of quantum-well (QW) and quantum-dot (QD) lasers is presented. We point out the differences between the gain function of a QD laser and a QW laser and give a qualitative description of the effect that leads to the high wavelength stability of QD lasers. Further- more, we demonstrate, by means of the gain spectra of an InGaAs and AlInGaAs QD laser, that devices with a high wavelength sta- bility can be manufactured over a wide range of emission ener- gies. The experimentally obtained data are fitted with a theoretical model that describes the gain of a QD ensemble. The characteristic features resulting in the high wavelength stability of QD lasers of 0.072 nm/K are analyzed and discussed. Index Terms—Gain measurement, modal gain, molecular beam epitaxy (MBE), self-assembled quantum dots (QD), semiconductor lasers, temperature stability. I. INTRODUCTION S INCE THE first realization of quantum-dot (QD) lasers about ten years ago, the device performance has been in- creased steadily. Today the device properties of QD lasers and quantum-well (QW) lasers are comparable in most fields [1], [2]. Moreover, in some fields, QD lasers show advantages over QW lasers, e.g., lower threshold current densities [3], [4], a broad gain profile [5], and superior characteristic temperatures [6]. It was also reported that QD lasers can exhibit a much higher temperature stability of the wavelength than comparable QW lasers [7]–[11]. This high wavelength stability was also already utilized in high-power pump lasers to reduce cost-intensive tem- perature stabilization [12]. However, there are only few publica- tions that try to give an explanation of this effect [9], [10]. Thus, there is a demand for a deeper understanding of the underlying principles. Thomson et al. attributed the improved temperature stability of the wavelength to a fortuitous matching of the QD energy-level distribution and the thermal evolution of the Fermi function [10]. This would suggest that devices cannot inten- tionally be tailored to be temperature-insensitive in a straight- forward way. We follow another approach and explain the en- hanced temperature stability by differences in the shape of the Manuscript received June 8, 2007; revised September 10, 2007. This work was sup- ported in part by the European Union under Project BrightEU. The authors are with the Technische Physik, Physikalisches Institut, Univer- sität Würzburg, D-97074, Würzburg, Germany (e-mail: ralph.debusmann@physik. uni-wuerzburg.de; Thomas.Schlereth@physik.uni-wuerzburg.de; Sven.Gerhard@ physik.uni-wuerzburg.de;Wolfgang.Kaiser@physik.uni-wuerzburg.de; Sven.Höfling@ physik.uni-wuerzburg.de; Alfred.Forchel@physik.uni-wuerzburg.de). Color versions of one or more of the figures in this paper are available online at http:// ieeexplore.ieee.org. Digital Object Identifier 10.1109/JQE.2007.911693 modal gain functions between QW and QD lasers in accordance with [9]. Based on our results, we report in this paper a universal approach to tailor QD lasers with temperature-stabilized wave- length. We report a direct comparison of QW and QD lasers and a QD device with the highest temperature insensitivity of the wavelength (0.072 nm/K) reported so far for lasers without wavelength-stabilizing elements. Within the macroscopic laser theory, the origin of this high temperature stability of our QD lasers is explained, and a theoretical gain model is compared with experimentally attained gain curves. This paper is organized as follows. Section II summarizes some fundamentals of semiconductor lasers. Section III pro- vides information on the practical realization of the QD and QW lasers and their characterization. In Section IV, the temperature stability of the lasers is investigated and explained. Section V concludes this work. II. THEORY A. Threshold Condition and Operation Point of a Semiconductor Laser The general threshold condition for a semiconductor laser can be written as [13] (1) where and are the internal and mirror losses, respectively, that can also be expressed in terms of the reflectivity of the res- onator mirrors and and the resonator length . is the optical confinement factor. Laser operation starts when the threshold condition (1) is sat- isfied, i.e., when the modal gain compensates the sum of all losses. Since the modal gain is a function of the photon en- ergy, the threshold condition (1) is reached at a specific energy first, i.e., when the maximum of equals for (see the inset Fig. 1). If we consider resonators with very narrow mode spacing, i.e., large cavity lengths, the photon en- ergy at this maximum represents also the emission energy. Thus, the lasing wavelength at can be determined by the intersec- tion of the sum of all losses with the peak gain , which represents the maximum of as a function of en- ergy (as illustrated in Fig. 1). For a QW laser, the gain above threshold remains at its threshold value [13]. To a good ap- proximation, this should also be true for the peak gain of a QD laser. Thus, changes in the laser emission energy are caused by changes in the intersection of with (i.e., the operation point). 0018-9197/$25.00 © 2007 IEEE