SEMICONDUCTOR DEVICES

Comprehensive and fully self-consistent modeling of modern semiconductor lasers

W. Nakwaski and R.P. Sarzała

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 Corresponding author: W. Nakwaski, Email: wlodzimierz.nakwaski@p.lodz.pl

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Abstract: The fully self-consistent model of modern semiconductor lasers used to design their advanced structures and to understand more deeply their properties is given in the present paper. Operation of semiconductor lasers depends not only on many optical, electrical, thermal, recombination, and sometimes mechanical phenomena taking place within their volumes but also on numerous mutual interactions between these phenomena. Their experimental investigation is quite complex, mostly because of miniature device sizes. Therefore, the most convenient and exact method to analyze expected laser operation and to determine laser optimal structures for various applications is to examine the details of their performance with the aid of a simulation of laser operation in various considered conditions. Such a simulation of an operation of semiconductor lasers is presented in this paper in a full complexity of all mutual interactions between the above individual physical processes. In particular, the hole-burning effect has been discussed. The impacts on laser performance introduced by oxide apertures (their sizes and localization) have been analyzed in detail. Also, some important details concerning the operation of various types of semiconductor lasers are discussed. The results of some applications of semiconductor lasers are shown for successive laser structures.

Key words: semiconductor laserssimulation modelEELVCSELVECSELDBFQCL



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Fig. 1.  Power balance of a diode laser[1].

Fig. 2.  Schematic structures of typical semiconductor lasers: one symmetrical half of EEL and QCL as well as VCSEL and optically pumped VECSEL with an external mirror.

Fig. 3.  Excitation of many longitudinal modes in a cavity of an edge-emitting laser. $g$ is the optical gain, $g_{\rm th}$ is the threshold gain, and $\lambda $ is the wavelength.

Fig. 4.  The spectral hole burning effect. $g_{\rm th1}$ and $g_{\rm th2}$ are the threshold gains of the first and the second, respectively, laser modes excited for corresponding wavelengths $\lambda_1$ and $\lambda_2$.

Fig. 5.  Temporal very short excitations of various longitudinal modes giving a multi-mode averaged spectral characteristic.

Fig. 6.  Flow charts of the self-consistent threshold calculation algorithms for (a) VCSELs and (b) VECSELs.

Fig. 7.  Maximal RT CW threshold optical gain $g_{\rm th,max}$ (solid line) and the wavelength $\lambda $ of the emitted radiation (dashed line) of the indicated lowest-threshold LP modes determined for the 20 $\mu $m diameter 1.5$\lambda $-cavity GaInNAs/GaAs QW VCSEL as a function of the distance of the oxide aperture from its anti-node position within a laser cavity[29].

Fig. 8.  (Color online) The structure of the 1.3-$\mu $m 3$\lambda $-cavity separate-confinement-oxidation (SCO) QW VCSEL.

Fig. 9.  An impact of the radius $r_{\rm E}$ of the electrical aperture on the RT CW maximal threshold gain $g_{\rm th,max}$ and the threshold current $I_{\rm th}$ of the indicated lowest-threshold LP modes determined for the large-size 20-$\mu $m diameter SCO VCSEL[29].

Fig. 10.  A mesa structure of the 1.3-$\mu $m top-emitting oxide-confined In (Ga)As/GaAs QD GaAs-based VCSEL.

Fig. 11.  RT (18 ℃) CW light-current characteristic of the 10-$\mu $m diameter 1.3-$\mu $m InAs/GaAs QD GaAs-based OC VCSEL. Crosses: experimental points. Lines: theoretical curves. Dash line: the LP$_{01}$ mode, dot-dash line: the LP$_{11}$ mode, solid line: both the LP$_{01}$ and the LP$_{11}$ modes. Exactness of an output power measurements is not worse than 0.01 mW and that of an operation current, 0.1 mA[34].

Fig. 12.  A dependence of the RT (18 ℃) CW threshold currents $I_{\rm th}$ of the 1.3-$\mu $m InAs/GaAs QD GaAs-based OC VCSEL on diameters $D_{\rm A}$ of their active regions. Crosses: experimental points. Dash line: simulation curve. Exactness of the diameter $D_{\rm A}$ seems to be not better than about 2 $\mu $m because a final shape of an oxide aperture is not a perfect circle, but it resembles rather an ellipse[34].

Fig. 13.  Nitride VCSELs. (a) VCSEL made by Nichia[36]. (b) VCSEL manufactured in Taiwan[37]. (c) VCSEL fabricated by the EPFL team from Switzerland[38].

Fig. 14.  Refractive-index and mode-intensity profiles within the laser cavity and DBRs[39]. (a) VCSEL made by Nichia[36]. (b) VCSEL manufactured in Taiwan[37]. (c) VCSEL fabricated by the EPFL[38]. Expanded profiles within active regions are additionally shown in Figures 14(d)-14(f).

Fig. 15.  A structure of the oxide-confined 1.3-$\mu $m QD (InGa)As/GaAs edge-emitting laser.

Fig. 16.  Distributions of the TE modes (the fundamental TE$_{00}$ as well as the first order TE$_{01}$ and TE$_{10}$ modes) within the cavity of the oxide-confined 1.3-$\mu $m QD (InGa)As/GaAs edge-emitting laser for the active-region width equal to 5 $\mu $m[24].

Fig. 17.  Maximal temperature increase $ T_{\rm max}$ versus pumping diameter $D_{\rm P}$ for different laser configurations: with the upper heat spreader (UHS), with the bottom heat spreader (BHS) and with the double heat spreader (DHS). The average pumping power is kept constant and is equal to 4.5 $\times$ 10$^{8}$ W/m$^{2}$[42].

Fig. 18.  A structure of an epi-up 7-emitter-array on a copper heat sink. The inset shows calculated room-temperature values of the thermal conductivity $\kappa_{\rm RT}$ (dotted line) and electrical conductivity $\sigma_{\rm RT}$ (solid line) in the symmetry plane of a single emitter.

Fig. 19.  Temperature along the QCL axis perpendicular to layer boundaries determined for the laser front mirror and somewhere within the laser central part[47].

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    Received: 13 October 2015 Revised: Online: Published: 01 February 2016

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      W. Nakwaski, R.P. Sarzała. Comprehensive and fully self-consistent modeling of modern semiconductor lasers[J]. Journal of Semiconductors, 2016, 37(2): 024001. doi: 10.1088/1674-4926/37/2/024001 W. Nakwaski, R.P. Sarzała. Comprehensive and fully self-consistent modeling of modern semiconductor lasers[J]. J. Semicond., 2016, 37(2): 024001. doi: 10.1088/1674-4926/37/2/024001.Export: BibTex EndNote
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      W. Nakwaski, R.P. Sarzała. Comprehensive and fully self-consistent modeling of modern semiconductor lasers[J]. Journal of Semiconductors, 2016, 37(2): 024001. doi: 10.1088/1674-4926/37/2/024001

      W. Nakwaski, R.P. Sarzała. Comprehensive and fully self-consistent modeling of modern semiconductor lasers[J]. J. Semicond., 2016, 37(2): 024001. doi: 10.1088/1674-4926/37/2/024001.
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      Comprehensive and fully self-consistent modeling of modern semiconductor lasers

      doi: 10.1088/1674-4926/37/2/024001
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      • Corresponding author: Email: wlodzimierz.nakwaski@p.lodz.pl
      • Received Date: 2015-10-13
      • Published Date: 2016-01-25

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