MODELING AND SIMULATION STUDIES OF VARIOUS n-DBR MATERIALS FOR 1.55 M VCSELS DIODE
Mohd Sharizal Alias, Burhanuddin Kamaluddin and Muhamad Rasat Muhamad
SolidState Research Laboratory, Physics Department, University of Malaya,
50603 Kuala Lumpur
ABSTRACT
Distributed Bragg Reflector (DBR) mirrors are key component in Vertical Cavity Surface Emitting Lasers (VCSELs) for 1.55 m wavelength optical-fiber communication application. This paper presents modeling and simulation studies of n-DBR mirrors comprises from epitaxial mirrors such InGaAsP/InP and GaAs/AlGaAs, as well as dielectric mirror of novel combination like Si-C/MgO. Simulation results and analysis for the reflectivity spectrum and absorption coefficient are reported and compared for each material.
INTRODUCTION
One of the key advances in optoelectronics and photonics technology in recent years is the development of VCSELs. Long wavelength (1.3 – 1.55 m) VCSELs are promising new generation of light sources for long-distance optical-fiber communication systems. It was first invented in 1977, using 1.3 m InGaAsP/InP material [1]. Figure 1 shows a schematic diagram of basic VCSELs design. VCSELs have many potential advantages compared to conventional edge emitting lasers (EELs). VCSELs exhibit advantages in high fiber coupling efficiency, low threshold operations, high modulation bandwidths, single mode operation, and the practical ability to be produced in large arrays. In addition, VCSELs offer the manufacturing advantages of wafer-scale fabrication and test, where the design allows the chips to be manufactured and tested on a single wafer.
Figure 1Basic schematic VCSELs design
In spite of this, VCSELs at long wavelength are much harder to fabricate than the short wavelength regime (0.85-0.98 m), which have been manufactured commercially. The principle obstacle is finding a high quality lattice matched DBR mirror system that can be integrated with InP-based active regions.These mirrors have to exhibit high reflectivities, high conductivities and low thermal resistance. Many different mirror systems have been proposed and demonstrated for long wavelength VCSELs. They can be classified into three main categories: epitaxially-grown, wafer-fused and dielectric-deposited. In this paper, we modeled and simulated the performances and characteristics of InGaAsP/InP, GaAs/AlGaAs and Si-C/MgO material systems, which representing each mirror group.
MODELING AND SIMULATION METHOD
The modeling and simulation is done by using HS_Design version 1.0 [2], which is a powerful and user friendly computer aided engineering software in designing photonics devices. Various standard methods can be use to calculate the optical characteristics of entire multi-layer device structure. The simplest and very powerful one is the Transfer Matrix Method (TMM) which is applied in the HS_Design Simulator. The starting point is the system of Maxwell equations written down (in frequency domain) as:
(1)
where and are the Fourier components of the electric and magnetic field, respectively, and is the tensor of the complex permittivity, all at a frequency . Semiconductor heterostructures used in photonics area, in fact, optically anisotropic structures even though they are made up from the cubic semiconductor materials. This is due to quantum wells (QW) layers, where its electronic and hence optical properties are different in the directions parallel and perpendicular to the direction of epitaxial growth. Assuming that all the layers are homogenous in a plane perpendicular to this direction (z-coordinate), the complex permittivity tensor is taken as:
(2)
Here, and are the complex permittivities in the directions perpendicular and parallel to the axis of symmetry (direction of growth), respectively. Then, in the j-th layer positioned between and, where dl is the width of I-th layer and widths of both the substrate and superstrate are set to zero, the vectorical fields in both the TE (electric field in the plane perpendicular to z) and TM (magnetic field in the plane perpendicular to z) polarizations can be expressed through a single scalar function:
(3)
is the in-plane propagation constant, common to all the layers, is the z-direction propagation constant in j-th layer, and are the amplitudes of forward and backward propagating waves, respectively. Propagation constant, and the components of the electromagnetic field in the j-th layer all are given in the Table 1 for both the TE and TM polarizations. Equation (3) together with Table 1 represents the exact solution of equations (1) in every single layer with the complex permittivity of the type equation (2).
Table 1 Propagation constant in the direction of growthand electromagnetic field components
Parameter / TE-polarization / TM-polarization/ 1 /
/ 0 /
/ / 0
At the interfaces, standard boundary conditions for electric and magnetic fields yield the following transfer relationships for the scalar function (3) and its derivative:
(4)
where the factor is defined in the Table 1. Combining equation (3) and (4), the amplitudes of the forward and backward propagating waves are transferred across the interface by
(5)
where is a square 2x2 complex transfer matrix:
(6)
All the relevant information regarding the optical properties of the layers is contained in the complex parameters and, which are defined as follows:
(7)
The amplitudes of the plane waves in superstrate and substrate are connected through multiplication of the matrixes (6):
(8)
Once the boundary conditions away from the structure, example, in the substrate and superstrate, are specified, the TMM gives the optical field distribution over the entire device. It is an extremely useful method, can be employed either in vertical or waveguide (is the complex propagation constant of the confined modes) configurations. As for this paper, the device studied is in a vertical configuration,as shown in Figure 2. Reflection, transmission and absorption spectrum, along with the optical field and light intensity distribution characteristics across the structure are calculated.
Figure 2Vertical configurations in HS_Design Simulator
The boundary conditions are formulated assuming that z-coordinate is measured up from the substrate while the light is incident down from the superstrate:
(9)
Fand Bare described above as in equation (3), with the subscripts “n+1” and “0” indicating the superstrate and substrate. Respectively, rand tare the reflection and transmission amplitude coefficients. These parameters are expressed through the components of the transfer matrix defined by equation (8):
(10)
The field distribution in every layer is given by equation (3), with amplitudes of the forward and backward propagating waves obtained by successive employing the equation (5) and (6). The intensity coefficients of reflection and transmission are calculated as:
(11)
The absorption coefficient of the vertical stack, which is defined as the fraction of light absorbed in the entire space between substrate and superstrate, is given by:
(12)
RESULTS AND DISCUSSIONS
Results show spectrum of reflectivity, DBR maximum reflectivity versus number of mirror periods and absorption coefficients for InGasAsP/InP (epitaxial), GaAs/AlGaAs (wafer-fused) and Si-C/MgO (dielectric) material systems, respectively. Figure 3 shows the reflectivity spectrum for each material system.
Figure 3: Reflectivity spectrum for each material system
The spectrum of all the material systems are periodic, with the reflectivity peak repeats every odd multiple of the Bragg frequency [3]. This reflectivity spectrum exhibit complicated phase and amplitude spectrum due to its distributed multi-reflection nature. By spacing multiple high-to-low index interfaces a distance /2 apart, the reflectivity of each interface adds constructively to produce mirrors with maximum reflectance of greater than 99% with a phase exactly zero or . Multiple reflections at the interfaces of the DBR and constructive interference of the multiple reflected waves increase the reflectivity with increasing number of pairs. The DBR is usually designed for a high reflectivity of >99% to overcome the short gain length cavity due to the small active region volume [4]. Table 2 listed the parameters and results for all the material systems.All of the mirror systems exhibit highest reflectivity at 1.55 m which corresponds to the emission wavelength of the VCSELs device.
Table 2: Parameters and results
Material system / InGaAsP/InP / GaAs/
AlGaAs / Si-C/
MgO
Parameter
Number of period (n) / 27.5 / 20.5 / 9.5
Thickness of each
period, d (m) / 0.112/
0.121 / 0.117/
0.130 / 0.1116/
0.2836
Doping Concentrations of
each period,Nd (x1016cm-3) / 1/0.5 / 1/0.5 / undoped
Maximum Reflectivity, Rmax (%) / 99.618388 / 99.674176 / 99.774734
Rmax Wavelength (m) / 1.55 / 1.55 / 1.55
Figure 4 shows a comparison between reflectivity dependence on number of mirror periods for the three material systems. It is clear that because of a smaller refractive index ratio between InGaAsP and InP (n≈0.28), this mirror system requires twice as many periods to reach a specified reflectivity as the GaAs/AlGaAs (n≈0.33) one at the same wavelength. The Si-C/MgO material combination, in contrast, requires even fewer numbers of periods because the refractive index ratio is much larger between the two materials (n≈0.79).
Figure 4: Calculated reflectivity of the three material systems
Figure 5 shows the absorption coefficient, for each material system. The InGasAsP/InP system and GaAs/AlGaAs system has the same absorption coefficient value that is =16.56583 cm-1. This could be attributed to theirsame optical properties as group III-V compound semiconductor materials.As for Si-C/MgO system, the absorption coefficient is slightly higher that is=16.58367 cm-1.
Figure 5: Absorption coefficient for each material system
In real DBR mirror systems, the reflectivity is reduced by the presence of material absorption [4] and light scattering [5], which marked itself as the saturation in the value of reflectivity in Figure 4. Material absorption has typically been the dominating mechanism, due to the small roughness of state-of-the-art semiconductor and dielectric mirrors technology used in VCSELs fabrication.Majority of work on 1.55 m VCSELs DBR mirror has been done in the InGaAsP/InP system with the best reported by [6] because of easier epitaxial growth due to its lattice matched with the InGaAsP active region, which is commercially used for this operating wavelength.However, the relatively small index contrast between InGaAsP and InP demand growth of a large number of periods before reaching acceptable reflectivities which makes it a challenge for the epitaxial growth fabrication, besides increasing the resistance of the device and raises the threshold current. Several advanced concepts have been developed to overcome those limitations, such as using amorphous mirror materials with higher thermal conductivity (a-Si/Al2O3) [7] and (Si-C/MgO) [8-10], and using antimonide-based mirrors with AlGaAsSb/AlAsSb system [11,12]. So far the best performing VCSELs are fabricated using the wafer fusion technology by applying GaAs/AlGaAs system [13]. This device has high thermal conductivity and good optical properties with high index contrast thus fewer layers required to achieve high reflectivities.
CONCLUSION
Modeling and simulation of n-DBR materials for 1.55 m VCSELs diode have been successfully performed using the HS_Design v. 1.0. High reflectivity mirror systems have been obtained that are 99.618388% for InGaAsP/InP epitaxial mirror system, 99.674176% for GaAs/AlGaAs wafer-fused mirror system and 99.774734% for Si-C/MgO dielectric-deposited mirror system, withnumber of periods demonstrated are 27.5 periods, 20.5 periods and 9.5 periods,respectively. This surpassed the best reported studies by [6], [13] and [10] for each material system.
ACKNOWLEDGEMENT
The work was sponsored by Ministry of Science, Technology and Environment of Malaysia under IRPA grant No. 09-02-03-0138. One of the authors (Mohd Sharizal Alias) thankfully acknowledges National Scientific Fellowship for awarding financial support to him within the duration of this work.
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