A physical model of quantum cascade lasers: Application to GaAs, GaN and SiGe devices

Abstract

Article:Harrison, P., Indjin, D., Jovanovic, V.D. et al. (7 more Harrison, P. and Indjin, D. and Jovanovic, V.D. and Mircetic, A. and Ikonic, Z. and Kelsall, R.W. and McTavish, J. and Savic, I. and Vukmirovic, N. and Milanovic, V. (2005) The philosophy behind this work has been to build a predictive 'bottom up' physical model of quantum cascade lasers (QCLs) for use as a design tool, to interpret experimental results and hence improve understanding of the physical processes occurring inside working devices and as a simulator for developing new material systems. The standard model uses the envelope function and effective mass approximations to solve two complete periods of the QCL under an applied bias. Other models, such as k.p and empirical pseudopotential, have been employed in p-type systems where the more complex band structure requires it. The resulting wave functions are then used to evaluate all relevant carrier-phonon, carrier-carrier and alloy scattering rates from each quantised state to all others within the same and the neighbouring period. This information is then used to construct a rate equation for the equilibrium carrier density in each subband and this set of coupled rate equations are solved self-consistently to obtain the carrier density in each eigenstate. The latter is a fundamental description of the device and can be used to calculate the current density and gain as a function of the applied bias and temperature, which in turn yields the threshold current and expected temperature dependence of the device characteristics. A recent extension which includes a further iteration of an energy balance equation also yields the average electron (or hole) temperature over the subbands. This paper will review the method and describe its application to mid-infrared and terahertz, GaAs, GaN, SiGe cascade laser designs. Repository paper

III-nitride semiconductors for intersubband optoelectronics: a review

“…Researchers from the University of Leeds (UK) have engineered one of the first designs for GaN-based QCLs using a fully consistent scattering rate equation model [242], and an energy balance method [250]. Both electron-LOphonon and electron-electron scattering mechanisms are taken into account.…”

Combined rate equation and Monte Carlo studies of electron transport in a GaAs/Al0.45Ga0.55As quantum-cascade laser

“…In such a case, when the Boltzmann transport equation (BTE) theoretical framework can be applied, it is common to use the Monte Carlo (MC) method [8][9][10][11][12][13][14][15][16][17][18][19], which is recognized as one of the most powerful tools for investigating charge transport in semiconductor materials and devices. The rate equation (RE) method [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], often applied to the description of the properties of QCL structures is based on the same physical picture. The important point is that the RE algorithm is easier to implement and less demanding of computational time, at the price of an additional hypothesis about the shape of the electron distribution function, which is usually taken as a Fermi-Dirac distribution.…”

“…It seems to be interesting to compare the results of both methods and discuss how the observed discrepancies are explained by used approximations [20]. In reference [29] one can find another comparison of these methods for silicon based devices.…”

Application of multi-subband self-consistent energy balance method to terahertz quantum cascade lasers

“…Additionally, few comparisons between the results of SCEB models, which determine subband electron temperatures, and other modeling methods have been done. Comparisons have been made between an average electron temperature and a multi-subband electron temperature SCEB model [1,5], between an average electron temperature SCEB and a MC model [6,7], and between a multi-subband temperature SCEB and a MC model [5]. However, the multi-subband temperature SCEB and MC model comparison was done for a p-SiGe/Si material system.…”