SiC

Study of substrate modes in a (Al,In)GaN/SiC semiconductor laser using finite element approach Valerio Laino, Bernd Witzigmann Integrated Systems Laboratory, ETH Zurich - Gloriastrasse 35, CH-8092 Zurich, Switzerland Phone: +41 44 632 6664, email: [email protected]

Matthias Streiff Sensirion AG CH-8712 St¨afa/Zurich, Switzerland Adrian Bregy Synopsys Switzerland Ltd. Affolternstrasse 52, CH-8050 Zurich, Switzerland Andreas Witzig Institut f¨ur Solartechnik SPF, Hochschule f¨ur Technik Rapperswil HSR Oberseestrasse 10, CH-8640 Rapperswil, Switzerland Ulrich T. Schwarz Angewandte und Experimentelle Physik, Universit¨at Regensburg Regensburg, D-93040 Regensburg, Germany

Abstract— Penetration of the waveguide mode into the substrate has some effects in Nitride-based semiconductor lasers grown on Silicon Carbide while it is usually not a problem in Arsenide-based devices. We observe oscillations in the red part of the measured gain spectrum of an (Al; I n)GaN semiconductor lasers. These have been attributed to the presence of a standing wave in the substrate. We use a finite element approach to solve the Helmholtz equation and a complex notation for the dielectric function. Our intention is to estimate the effects of localized optical loss on the waveguide mode. In order to analyze measured oscillation in the Hakki-Paoli experiment we need to take into account optical loss in the P-doped region and in the substrate.

effect of the substrate on the active mode is much bigger in these devices compared to Arsenide-based lasers. This is due to the high refractive index of the substrate, that is comparable to the active region refractive index.

Index Terms— substrate modes, confinement factor, gallium nitride

I. I NTRODUCTION Substrate modes are commonly referred to as solutions of the Helmholtz equation that are spatially located in the substrate region. Manufacturers carefully design semiconductor laser to position one waveguide mode (fundamental mode) to have a large overlap with the active region in order to maximize optical gain. Despite the strong confinement, this mode extends also in the substrate. (Al; In)GaAs based semiconductor lasers are usually grown on GaAs substrates. For such devices, the refractive index of this region does not differ significantly from the epitaxially grown layers. This causes only a negligible portion of the waveguide mode to overlap with the substrate. Lasers emitting in the UV spectrum are manufactured with (Al; In)GaN compounds usually grown on a SiC substrate due to the lack of commercially convenient GaN wafers. The

Fig. 1. Measured optical gain for driving currents of 10mA to 100mA in steps of 10mA.

II. M EASUREMENTS AND SIMULATIONS We have Hakki-Paoli measurements of a laser diode working in the visible spectrum. The device is an edge-emitting laser, epitaxially grown by low pressure MOVPE on a SiC substrate. The structure consists of 900nm Al0:08 Ga0:92 N ncladding, 100nm n-GaN waveguide, the active region, 20nm AlGaN electron blocking layer, 100nm p-GaN contact layer. In the active region three 2nm In0:1 Ga0:9 N quantum wells

are separated by 6nm thick GaN barrier layers (see [1]). Measurements of optical gain show periodic oscillations on the red side of the spectrum mainly (see Fig. 1). Hakki-Paoli measurements allow estimating the net mode gain, including all the optical losses:

G=


g 

f ca



mirrors



substrate

(1)

where G is the measured gain, g is the material gain and is the fraction of the mode that overlaps with the optically active region. Our intention is to demonstrate that oscillations in the measured optical gain are due to variations in the optical loss. These are induced by changes of the portion of the waveguide mode that overlaps with the substrate. One-dimensional simulations of the optical intensity profile have already been performed using TMM technique (see [3] and [7]). In this contribution, we evaluate solutions of the Helmholtz equation using a finite element approach (see [2]). A vectorial formulation is applied to properly describe the interface between regions having different refractive indices. The complex notation of the dielectric function (see for example [4]) allows introducing optical loss for each region in the finite element description. Solutions of the Helmholtz equation consist of complex eigenvalues composed of a modal effective index as real part and a modal effective loss as imaginary part. The corresponding eigenvector is given by the vectorial electric field spatial distribution. The refractive index of SiC is reported to be around 2:75 for photon energies around 3eV while GaN compounds have refractive indices estimated to be around 2:5 for the same photon energy (see for example [7] and [8]). Due to refractive index of SiC , the waveguide mode is not the one with the highest effective index. Moreover both the eigenvalue and the confinement factor are a function of the excitation wavelength. With our formulation of the problem, we confirm the presence of a standing wave in the substrate. We show that oscillations of the modal loss versus excitation wavelength are a result of changes in the fraction of the mode that overlaps with the substrate. In this region, due to the high refractive index, the evanescent wave from the cladding excites a propagating wave that is reflected back from the bottom metal contact, leading to a standing wave between cladding-substrate interface and bottom metal contact. We found that the optical path length in the substrate is responsible for the distance in energy of two successive peaks in the optical loss spectrum. The dopant used in the P region of the device introduces localized optical loss and shifts the waveguide mode towards the substrate. This could be due to the high activation energy of Magnesium in GaN (see [5] and [6]). Our simulations show that the fraction of the waveguide mode that overlaps with the substrate increases from less than 3% to about 5% including optical loss in the P-doped region of the model. The magnitude of the optical loss oscillation versus excitation wavelength is determined by the amplitude of the standing wave in the substrate. This latter is given by the loss associated with SiC and by the fraction of the waveguide mode overlap-

Fig. 2.

Vertical profile of simulated optical intensity.

ping with this region. Our simulations show that using 10 4 as imaginary part of the refractive index for SiC amplitude of the in the optical loss is about 0:1cm 1 , while using 10 5 the oscillations are comparable to experiments. III. C ONCLUSIONS Using the finite element approach to solve the Helmholtz equation and a complex notation for the dielectric function, we analyze oscillations in the modal optical loss spectrum. Their period is related to the substrate thickness, while amplitude is given by a combination of the fraction of the waveguide mode penetrating into the substrate and optical loss of this layer. ACKNOWLEDGMENTS We want to thank the Swiss Commission for Technology and Innovation - CTI. R EFERENCES [1] U. T. Schwarz et al., Excitonic signature in gain and carrier induced change of refractive index spectra of (In,Al)GaN quantum well lasers, Applied Physics Letters, volume 85, number 9, 2004. [2] Matthias Streiff et al., Computing optical modes for VCSEL Device Simulation, IEE Proceedings on Optoelectronics, pp.166-173, August 2002. [3] U. T. Schwarz et al., Nitride-based in-plane diodes with vertical current path, Invited Paper, Proceedings of SPIE, Vol. 5365, 2004. [4] B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, Book, Wiley series in pure and applied optics. [5] W. Goetz et al., Activation of acceptors in Mg-doped GaN grown by metalorganic chemical vapor deposition, Appl. Phys. Lett. Vol. 68, No. 5, 29 January 1996. [6] W. Goetz et al., Activation energies of Si donors in GaN, Appl. Phys. Lett. Vol. 68, No. 22, 27 May 1996. [7] M. J. Bergmann, Optical-field calculation for lossy multiple-layer Alx Ga1 x N=Inx Ga1 x N laser diodes, Journal of Applied Physics, volume 84, number 3, 1998. [8] U. T. Schwarz et al., Optical gain, carrier-induced phase shift, and linewidth enhacement factor in InGaN quantum well lasers, Applied Physiscs Letters, volume 83, number 20, 2003.