WIAS-TeSCA simulations of laser diodes
Collaborator: U. Bandelow,
H. Gajewski,
A. Glitzky,
R. Hünlich
Cooperation with: F. Heinrichsdorff, N. Kirchstädter (LUMICS GmbH Berlin)
Supported by: LUMICS GmbH Berlin
Description:
The static and dynamic performance of laser diodes
is analyzed on the basis
of different models. The device simulator WIAS-TeSCA, [3],
uses two-dimensional models in the transverse
cross section combined with rate equations
in the longitudinal direction. Numerical solutions of these equations allow
for an exploration of a wide spectrum of lasing effects.
Figure 1 shows a schematic transverse cross section of a GaAs-based
high-power laser diode.
The colors indicate different materials, the lines represent the
intensity distribution of two optical modes.
The underlying model equations for the relevant electronic,
thermodynamic, and optical phenomena
form a system of nonlinear partial
differential and ordinary differential equations. The electronic
processes are described
by continuity equations for electrons and holes, and a Poisson equation for
the electrostatic potential
(drift-diffusion model). Thermodynamic
behavior is modeled by a heat flow equation
for the device temperature
(or equivalently by balance equations for the density of
the entropy or the internal energy), [1].
Finally, Helmholtz equations for different modes
of the transverse optical field and
corresponding photon balance equations in longitudinal direction
characterize the optical behavior, [2].
In this project we used our simulation tool WIAS-TeSCA to
calculate
stationary characteristics
for laser diodes of the company LUMICS GmbH.
For this purpose we solved the stationary equations to obtain
IU characteristics and PI characteristics. To give hints for the
development of new lasing structures we varied in our simulations
the geometry of the device,
the doping and the composition of the material
of relevant layers in the active
zone, especially the number of quantum wells.
Important parameters for laser operation are derived from the
PI characteristics (see left upper picture in Figure 2). Relevant
properties are, firstly,
the threshold current which is the minimum
injection current that is required for lasing to occur and,
secondly, the differential quantum efficiency which means the slope of the
characteristics near threshold.
These parameters depend strongly upon the temperature in the active zone
of the laser which has to be calculated, too.
Figure 2 illustrates simulation results for a
test structure for which the half transverse cross section is given in the
middle of the last line of pictures. The left upper picture shows
the PI characteristics. Here the second optical mode does not give a
relevant contribution to the optical output power.
The right upper picture contains the temperature
profile on the half transverse cross section. The middle upper
curve represents the optical gain along the quantum well. Here already the
saturation of gain under the ridge can be observed. The left lower
diagram contains the densities of electrons and holes in
a cross section along the y-axis
of the adjacent picture.
The right lower picture gives the electrostatic potential (black),
the position of the valence band and of the conduction band (green and red),
and the quasi-Fermi potentials of electrons and holes (blue and orange)
along the same cross section.
Fig. 2:
WIAS-TeSCA simulation of a ridge waveguide laser diode
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References:
- U. BANDELOW, H. GAJEWSKI, R. HÜNLICH,
Thermodynamics-based modeling of edge-emitting quantum well lasers,
in preparation.
- U. BANDELOW, R. HÜNLICH, TH. KOPRUCKI,
Simulation of static and dynamic properties of edge-emitting
multiple-quantum-well lasers,
IEEE J. Select. Topics Quantum Electron., 9 (2003), pp. 798-806.
- WIAS-TeSCA. http://www.wias-berlin.de/software/tesca, 2003.
LaTeX typesetting by I. Bremer
2004-08-13