InGaN/GaN Ridge Type with MQW Laser Diode Simulation Using ATLAS

 

Introduction

The light source on short wavelenghts has been researched in GaN-based lser diodes (LDs). For high efficiency emitting devices, the wave-guide layer has been investigated to obtain more stable far field patterns and the multi-quantum well layers have been researched as a means of acheiving high quantum efficiency in blue-violet lasers.
In this paper, we demonstrate simulation results showing that the behavior of far field patterns depends on the transverse mode with 3 types of waveguide layers and also the quantum effects on the optical gain and the carrier distribution with the multi-quantum well layers.

 

Transverse Modes Analysis

The transverse mode control is one of the important concerns in optical disk applications. In InGaN lasers, the waveguide layer is designed to obtain a stable guided mode[1][2]. We analyzed the waveguide structure of an InGaN/GaN-based MQW laser as shown in Table 1, and a 3um ridge type waveguide.

Table I. Layer thickness and parameters of the laser diode.

 

With the scalar Helmholtz equation[3], the guided mode and FFP have been analyzed using a complex refractive index using ATLAS. In Figure 1 the AlGaN waveguide layer has 0.3um. Figure 1. (a) shows the 2 dimensional guided mode and 1 dimensional optical intensity along the center of the laser diode. Figure 1(b) shows the far field pattern. In this case, the guided mode including the oscillation waveguide mode, which has the maximum confinement factor in the MQW region, becomes the high-order mode. For this reason, the far field pattern has two peaks as shown in Figure 1(b), which is not suitable for optical disk usage.

Figure 1. Waveguide analysis structure with 0.3um waveguide layer thickness. (a) Guided mode and 1Dimensional optical intensity along the center of laser (b) Far Field Pattern.

To suppress this oscillation mode, the waveguide thicknesses selected are 0.5 and 1.0 um. Figures 2 and 3 show waveguide layer thicknesses of 0.5um and 1.0um respectively.

 

Figure 2. Analyzed guided mode in ridge type laser with 0.3um waveguide layer thickness. (a) Guided mode and 1 Dimensional optical intensity along the center of laser. (b) Far Field Pattern.

 

Figure 3. Analyzed guided mode in ridge type laser with 1.0um waveguide layer thickness. (a) Guided mode and 1 Dimensional optical intensity along the center of laser. (b) Far Field Pattern.

 

With the complex index model, the guided mode and far field pattern has been analyzed accurately using ATLAS.

 

Gain Model and Quantum Potential Model

For the Strained Wurtzite crystal, ATLAS supports the Three-Band Model for Gain and Radiative Recombination which is derived from the k.p method[3]. This optical gain, as shown in Figure 4, provides a link between optical and electrical models. The optical local gain depends on the qusi-Fermi levels, which in turn impact dielectric permittivity, and on the coupling between the stimulated carrier recombination rate(Rst) and the density of the photon(S).

Figure 4. Local optical Gain for In0.2GaN Wurtzite crystal.

To determine the photon density, ATLAS solves the system of photon rate equations, which includes the modal gain and modal spontaneous emission rate. The line width of the laser mode is one of the key parameters for the laser diode. In the photon lifetime modal rate equation, the laser losses include the mirror loss, absorption loss and internal user-defined loss.

The effects due to confinement of carriers associated with variations of local potential on the scale of the electron wave functions (quantum effects) can be modeled in ATLAS using the Bohm Quantum Potential (BQP) model. This BQP model has better convergence properties in many structures and it can be calibrated against results from the Schrodinger-Poisson equation as like the MQW structure. Figure 5 shows the calibration of the BQP parameters to match the Schrodinger-Poisson analysis.

Figure 5. Calibrated carrier concentration on 2 MQW layer In0.2GaN/GaN.

 

Device Structure and Parameters

For optical and carrier confinement, the width of the ridge is 3.0um on the top the cleaved front facet has a power reflectivity of Rf=18%, the back facet is coated for high reflectivity of Rr=95%, and the cavity length is 450um.

The carrier drift-diffusion model and quantum potential model was combined to obtain the accurate carrier density. The incomplete ionization of dopant effect is also considered. In this simulation, the defect related recombination, SRH model was chosen with a carrier lifetime of 1ns. A spontaneous emission parameter of was chosen as 2e-11 cm3s-1. The auger recombination model was chosen with 1e-34 cm6s-1 for GaN.

ATLAS supports the mirror boundary condition for symmetrical device structure at the center of the device. This allows the laser diode to be simulated with only the right side but still providing complete laser characteristics. The NFP and FFP are output like the full structure.

Figure 6 shows the half of the ridge type FP laser diode device structure. In this structure, the GaN waveguide layer selected has 1um thickness which is the most stable for the transverse mode, and two pairs of InGaN/InGaN well and barrier layers for the MQW active layers.

 

Figure 6. Ridge type GaN/InGaN laser diode structure.

 

Results and Discussion

Optical reflection and waveguiding mainly depends on the refractive index profile of devices. The refractive index was calculated using Adachi’s fomula [3]. The vertical index profile of the laser is plotted in Figure 7 with the normalized optical intensity.

 

Figure 7. Refractive index and normalized optical intensity.

 

Polarization modeling is critical for GaN based devices. The spontaneous polarization as well as strain-induced polarization in nitride compounds results in polarization charges at the hetero-junction and in built-in polarization fields. The scale parameter for polarization was chosen with 0.3 in this simulation for a more close simulation of the real device. The quantized carrier concentration stands on the edge of the band in quantum well layers, this is caused by the polarization effects to the Band tile as shown in Figure 8.

 

Figure 8. Band structure and carrier density with 30% of polarization charge at the threshold current.

 

Figure 9. Longitudinal mode for the FP laser at the threshold current.

 

ATLAS can consider the multi-transverse mode and multi-longitudinal mode for the FP type laser diodes. At the low current density, the longitudinal mode is lasing widely with the mode spacing depending on the cavity length. In this structure with a 450um cavity, the mode spacing was originally 0.81A, but in this FP type laser case the spacing was widened to 1.43nm to save simulation time. The lasing wavelength is 432nm.

With 2 transverse mode simulating, the Nea Field and Far Field Patterns are as shown in Figure 10. The FFP has 28 degrees along the vertical angle and 8 degrees along the transverse on the fundamental mode.

 

Figure 10. NFP and FFP at the threshold current. 28 degree and 8 degree on the fundamental mode.

 

Figure 11. Current Light output power curve.

 

With the 3um width ridge type and 450um cavity length laser, and the 30% of the polarization effects, the threshold current is 22mA.

 

Conclusion

With ATLAS, the most important phenomena for the laser diode was analyzed from the transverse mode as waveguide, the carrier transport with quantum effect, and the gain distribution on the MQW. Finally the longitudinal multi mode was considered in addition to the near field pattern and far field pattern during the simulation. These capabilities are combined with the photon rate equation for the laser diodes in ATLAS.

 

Reference

  1. Gen-ichi Hatakoshi, et al,”Analysis of Device Characteristics for InGaN Semiconductor Lasers”, Jpn. J. Appl. Phys. Vol.38(1999) pp.1780-1785.
  2. Masaaki Onomura, et al, “Analysis of Transverse Modes of Nitride-Based Laser Diodes”, IEEE Journal of Selected Topics in Quantum Electronics, Vol.5, No.3, May/June 1999, pp.765-770.
  3. ATLAS User’s Manual, 2011.
  4. J.Piprek, et al, “Physics of high-power InGaN/GaN lasers”, IEE Proc.Optoelectron, Vol.149, No.4, August 2002, pp.145-151.

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