Nanoscale physics

Effect of losses in active region and the doping concentration on optical characteristics of quantum cascade laser
S.S. Kurlov1, 2, M.P. Semtsiv1, Z.Ya. Zhuchenko2, G.G. Tarasov2, W.T. Masselink1 
1 Department of Physics, Humboldt University Berlin, Newtonstr. 15, 12489 Berlin, Germany
2 Institute of Semiconductor Physics of the NAS of Ukraine,   pr. Nauki 45, 03028 Kyiv, Ukraine
 E-mail: kurlov@isp.kiev.ua

Quantum cascade lasers (QCLs) are unipolar intersubband devices using the electron transitions between the separated levels in specifically designed multiple-quantum-well heterostructures for operation. Recently they are realized for a wide range of wavelengths from the mid infrared to the terahertz spectral region. Main QCL characteristics such as the threshold current density, the optical slope efficiency, and the wallplug efficiency depend from doped electron concentration and losses in active region of laser structure. Moreover these characteristics depend substantially from temperature. Typically the temperature dependence of threshold current density Jth(T) in the mid-infrared QCLs is characterised  by special temperature T0 in Jth(T)= J0exp{T/T0}. The optical slope efficiency dP/dI is described by equation: dP/dI(T)= Cexp{-T/T1} with T1 being a characteristic temperature, and the wallplug efficiency is presented by with  as the electrical input power and as the is the optical power output. 
We developed a temperature dependent  scattering-rate model including various scattering mechanisms such as the longitudinal optical phonon, interface roughness, and acoustic phonon scatterings entering the total intersubband scattering rate in order to extend the model for a wide temperature range. It has been shown that the model allows the efficient calculation of the gain characteristics and current densities due to a substantial reduction of numerical effort in case of various types of QCLs. Basing on the developed approach we analyze the characteristic temperatures T0 and T1 as well as the  value with account on the losses in active region and the doping concentration for a number of active region designs and compare them with the experimental data.