IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 40, NO. 7,JULY 2004 833 Effect of Internal Optical Loss on Threshold Characteristics of Semiconductor Lasers With a Quantum-Confined Active Region Levon V. Asryan and Serge Luryi, Fellow, IEEE Abstract—We develop a general approach to including the in- ternal 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 param- eters, the constant component and the net cross section for all ab- sorption loss processes. We show that, in any structure where the free-carrier density does not pin in the presence of light genera- tion, the free-carrier-density dependence of internal loss gives rise to the existence of a second lasing threshold above the conventional threshold. Above the second threshold, the light–current charac- teristic 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. Index Terms—Quantum dots (QDs), quantum wells (QWs), quantum wires (QWRs), semiconductor heterojunctions, semi- conductor lasers. I. INTRODUCTION I NTERNAL optical loss is present in all types of semicon- ductor lasers. It adversely affects their operating character- istics—increasing the threshold current density and decreasing the differential efficiency [1]–[3]. Because of the lower value of the optical confinement factor for thin layers, the effect of in- ternal loss is stronger for lasers with a reduced-dimensionality active region than for bulk lasers [1]. In general, several mechanisms can contribute to the internal loss, such as free-carrier absorption in the optical confinement layer (OCL) and in the cladding layers (emitters) [4], interva- lence band absorption (hole photoexcitation into the split-off subband) [5]–[8], carrier absorption in the quantum-confined active region itself, and scattering at rough surfaces and imper- fections of the waveguide. Determination of the absorption co- Manuscript received January 26, 2004; revised April 2, 2004. This work was supported in part by the Air Force Office of Scientific Research Multidisci- plinary University Research Initiative Program, Award no. F49620-00-1-0331, managed by T. Steiner and in part by the New York State Center for Advanced Sensor Technology. L. V. Asryan is with the State University of New York at Stony Brook, Stony Brook, NY 11794-2350 USA, on leave from the Ioffe Physico-Technical Insti- tute, St. Petersburg 194021, Russia (e-mail: asryan@ece.sunysb.edu). S. Luryi is with the State University of New York at Stony Brook, Stony Brook, NY 11794-2350 USA (e-mail: Serge.Luryi@sunysb.edu). Digital Object Identifier 10.1109/JQE.2004.830207 efficient for each of these processes is very important because, depending on their relative strengths and the structure design parameters, the net absorption loss coefficient can be as low as 1.4 cm [9] or as high as 20 cm [10], and even higher [11]. Due to the variety of possible mechanisms, one hardly ex- pects a first-principle evaluation of the net internal loss coeffi- cient. Formally, however, all different processes can be grouped into two categories, one dependent on the injection carrier den- sity (such as free-carrier absorption in the OCL), the other in- sensitive to this density (such as scattering at rough interfaces). Leaning upon this fact, we develop here a general phe- nomenological approach to the inclusion of the effect of internal loss on threshold characteristics in semiconductor lasers. We show that the injection-carrier-density dependence of internal loss coefficient, combined with nonpinning of the carrier density, gives rise to the existence of a second lasing threshold above the conventional threshold; above the second threshold, the light–current characteristic is two-valued. We also show that the presence of internal loss narrows consider- ably the region of tolerable structure parameters in which the lasing is attainable. The total net internal loss coefficient (which we shall refer to as the internal loss) is presented as the sum of a constant and a component linear in the carrier density in the OCL as follows: (1) where can be viewed as an effective cross section for all absorption loss processes. The assumption of a linear dependence on the free-carrier density in the waveguide is justified in most situations of practical interest. For example, intervalence band absorption increases proportionally to hole density [5]–[7]; free-carrier absorption also increases linearly with [4]. The carrier densities in the cladding layers, being mainly de- fined by the doping levels there, remain practically unchanged and close to their built-in values as the injection current varies. 1 For this reason, the free-carrier and the intervalence band absorption loss due to the optical mode penetration into the cladding layers are both lumped into the constant component of the internal loss. 1 There may be a slight increase in the carrier density above their built-in values in the cladding layers due to the carrier leakage from the OCL at high injection level and high temperature. In the first approximation, this variation should also linearly follow the carrier density in the OCL . Hence, the inclu- sion of this effect will slightly increase the value of in (1). 0018-9197/04$20.00 © 2004 IEEE