Differential gain in InGaAsN quantum well structures (Regular Paper) M.S. Wartak Senior Member IEEE Department of Physics and Computer Science Wilfrid Laurier University Waterloo, Ontario N2L3C5, Canada Email: mwartak@wlu.ca Telephone: (519) 884-1970, ext.2436 Fax: (519) 746-0677 P. Weetman Department of Physics and Computer Science Wilfrid Laurier University Waterloo, Ontario N2L3C5, Canada Email: pweetman@eml.cc Telephone: (519) 884-1970, ext.2685 Fax: (519) 746-0677 Abstract— Numerical studies of differential gain in InGaAsN quantum well systems are reported. Our approach is based on 10 × 10 Hamiltonian solved self-consistently with the Poisson’s equation. It was found that the properties of that system can be effectively modified. The differential gain is one of basic parameters which characterize operation of quantum well (QW) based semicon- ductor lasers [1]. It is defined as the derivative of the optical material gain with respect to the injected carrier density. It is linked with the modulation bandwidth of these devices. The differential gain is often determined from measurements of the relaxation oscillation frequency as a function of the emitted optical power under the approximation of small signal modu- lation [2], [3]. The differential gain is an intrinsic property of the material in the active layer and is independent of the laser structure. In recent years we have witnessed tremendous progress in the research on a new class of materials based on ni- tride semiconductors [4], [5]. Dilute Nitride lasers based on GaAs are considered as replacements for InP based lasers in metropolitan and local area networks. It has been found that replacing a small amount of the group V element by nitrogen in a III-V material systems reduces the energy gap. This reduction significantly changes band structure and offers new possibilities of improving optoelectronic properties of devices based on those materials. For example, impressive improvements of in-plane lasers [6] and [7] as well a VCSELs [8] based on those materials have been reported. Differential gain of quantum well nitride structures have been studied recently [9]. It was found that differential gain with respect to either current or carrier concentration is re- duced in dilute-nitride devices. Differential gain among other factors was recently analyzed theoretically by Alexandropou- los and Adams [10] in the BAC model. It was found that an increase of Nitrogen content reduces the peak differential gain. We have extended their analysis to 10 × 10 Hamiltonian and also included electrostatic effects on the heterostructure potentials of electrons and holes. Our approach is based on a 10 × 10 k·p Hamiltonian [11] which is a generalization of the 8 × 8 L¨ uttinger-Kohn Hamiltonian [12] that accounts for coupling between the conduction and hole bands. Substitution of nitrogen splits the conduction band to create the additional ’nitrogen band’. This new system necessitates the introduction of an additional band in the description of the electron-hole bandstructure. For this purpose, a 10 × 10 Hamiltonian which accounts for nitrogen, conduction, light- and heavy-holes and spin bands is used here. We have recently applied 10 × 10 Hamiltonian [13] to nu- merically analyze the effective masses in InGaAsN quantum- well structures with self-consistent effects. In that paper we were able to obtain detailed band structures for various well parameters such as nitrogen compositions. We use this infor- mation in the material gain computations. The structure simulated is similar to that used previously [13] and consists of undoped In 0.36 Ga 0.64 As 1-y N y system. The Nitrogen composition (y) changes in the range 0.00 < y< 0.05. We have considered several values of well widths. We performed the following steps of our computations: 1. produce gain spectrum at a given temperature 2. determine differential gain at peak value 3. increase temperature and repeat process 4. plot differential gain such determined vs temperature. Below, we report on some representative results. In Fig.1 we plotted differential gain vs energy for two values of barrier composition and three values of well widths. One can observe that the effect of Nitrogen content in the barrier is relatively small for all well widths considered. One can also observe that by varying well width, we can significantly change maximum value of differential gain. Its peek value stays roughly the same at a particular energy. There is however optimum value of well width for which differential gain reaches maximum. In Fig.2 we plotted differential gain as a function of Nitrogen composition for four values of well width. As was noticed with data shown in Fig.1, for a given Nitrogen composition, that the value of differential gain is the largest for 6 nm well width. For all values of 664 13D2-5 12th Optoelectronics and Communications Conference/16th International Conference on Integrated Optics and Optical Fiber Communication (OECC/IOOC2007) Technical Digest, July 2007, Pacifico Yokohama