This paper involves the calculation for composition of different layer used in laser structure and the simulation of cavity, formed by creating air columns in the InGaAsP medium, for square lattice. The aim of this project is to fabricate approximately zero threshold current lasers. This project involves FDTD simulation for optimizing dimension of the device, fabrication of laser structure and finally characterization of the device structure.Singapore-MIT Alliance (SMA

Chua, Soo-Jin

Fitzgerald, Eugene A.

Vajpeyi, Agam P.

DSpace@MIT

 1 Singapore-MIT Alliance, Advanced Materials for Micro-and Nano-Systems Programme, 4 Engineering Drive 3,Singapore 1175762 Department of Electrical and Computer Engineering,National University of Singapore, 4 Engineering Drive 3,Singapore 1175763 Department of Material Science and Engineering,Massachusetts Institute of Technology, Cambridge,Massachusetts, USA 02139Abstract— This paper involves the calculation for compositionof different layer used in laser structure and the simulation ofcavity, formed by creating air columns in the InGaAsP medium,for square lattice. The aim of this project is to fabricateapproximately zero threshold current lasers. This projectinvolves FDTD simulation for optimizing dimension of the device,fabrication of laser structure and finally characterization of thedevice structure.Index Terms—Photonic band gap, zero threshold current,FDTD simulator.INTRODUCTIONPhotonics crystals relate to photon as semiconductor materialsare for electrons. Photonics crystal has a band structure thatcontains a photonics band gap due to the interaction ofphotons with a periodic potential, which is caused by thedifference in refractive index in the structure. The mainmotivation to work in PBG materials are minimum lossthrough tight bend and easy tailoring of photonic crystalproperties. Two-dimensional photonics crystal allows greatminiaturization in the design of Photonics integrated circuits,which will reduce the cost of future optical communicationsystem.Photonics crystals are two and three dimensionally periodicstructures with high refractive index contrast.  The existenceof a photonics band gap, a frequency range in whichpropagation of light is prevented in all directions, makes PBGstructures very useful in applications where spatiallocalization of light is required. When a point defect is created in a photonic crystal, it ispossible for that defect to pull a light mode into the band gap.Because such a state is forbidden from propagating in the bulkcrystal, it is trapped. The mode decays exponentially into thebulk. Such a point defect, or resonant cavity, can be utilized toproduce many important effects. Application of resonantcavities can be applied to enhance the efficiency of lasers;taking advantage of the fact that the density of states at theresonant frequency is very high (approaches a delta function). Photonics band gap properties can be tailored by changing –1. Lattice parameter of the crystal2. Radius of pillars or holes3. Refractive Index of the materialBy changing the size or the shape of the defect, photonic bandgap can be changed. By increasing the amount of dielectric inthe defect, one can pull down higher-order modes. The defectwas created by increasing the radius of the center rod. This makes PBG material very useful for the application.Various scientific and engineering applications, such ascontrol of spontaneous emission, zero-threshold lasing, sharpbending of light are expected by using the photonic band gapand the artificially introduced defect states and/or light-emitters.The vertical-cavity surface-emitting laser is now recognized asa very important light source for local area networks.However, there is a limitation of available power, typically toless than a few mill watts for complete single longitudinal andlateral-modes.   To overcome this problem, a square photonic crystal latticeis used in the laser structure. The PBG containing N-type InPsubstrate is bonded with InGaAsP/InP by using wafer fusiontechnique. Active layers contain multiple quantum well andquantum barrier sandwiched between N and P type InP layer.   The photonic crystal enabled them to form a stable laser [1]cavity in which the crystal controlled the propagation of lightin the X- and Y-directions, yielding a two-dimensionalstanding wave; the lattice points determine both the lasingwavelength and the beam pattern. Our aim is to design a newphotonic crystal laser for telecommunications applications. FDTD SIMULATION:FDTD simulator is used (Finite difference Time difference) tostudy the interaction of electromagnetic fields with two-dimensional PBG structures. The FDTD [2-3] simulator is afull-wave solution to the vector Maxwell equations. It canincorporate complicated scatterers and materials such as thePBG structures with great flexibility. In this manner, the basicelectromagnetic properties of the PBG structures can bedetermined over a broad bandwidth of frequencies in a singlerun. This allows a determination of the pass and stop bands ofthe PBG from an essentially impulse excitation of the PBGLaser Fabrication by Using Photonic Crystal                                 Agam.P.Vajpeyi1 , Soo Jin Chua 2 , Eugene Fitzgerald 3structure. The response of the same structure at selectedfrequencies, such as the resulting electric field patterns, canthen be evaluated in detail.Since the TE mode is a favorable mode for air columnsembedded in the dielectric medium so we are restricted to theTE polarization, which requires the Ey, Hx, and Hz fieldcomponents. The associated FDTD equations are obtainedwith the standard staggered grid, leap-frog time integrationscheme [4] and are given by the expressions-( )[ ]),(1,12221,2221, 2121kiEkiEzttkiHttkiH nynymnxmmnx −+∆∆+∆+ +∆+∆−= + −+ σµσµσµ( )[ ]),(,1122,2122,21 2121kiEkiExttkiHttkiH nynymnxmmnz −+∆∆+∆+ +∆+∆−= + −+ σµσµσµ( ) ( ) −−+∆∆+∆− −−+∆∆+∆+∆+∆−∆+∆−=++++++),21(),21(122)21,()21,(122),(22,22,21212121211kiHkiHxttkiHkiHzttkiJttkiEttkiEnxnzEnxnxEnyEnyEEnyσεσεσεσεσεThe superscript n labels the time steps while the indices i andk label. Where Є = dielectric constant of the medium           µ = magnetic permeability of the medium          Eσ =electrical conductivity of the medium          Mσ = magnetic conductivity of the medium           t∆ = increment step for time            x∆ = increment step along x direction             z∆ = increment step along z direction         Selection of Design ParameterThe aim is fabricate photonic cavity laser fortelecommunication wavelength i.e. 1.55 micron. Photoniccavity laser offers the benefit of low noise, due to compactsize, and high spontaneous emission coupling factor of themicro cavity. Flexibility in geometry allows fine tuning ofdefect mode radiation pattern as well as emission wavelength.This device is also useful where crystal growth of high indexcontrast mirrors is limited such as long wavelength verticalcavity surface emitting laser or blue green GaN based device[5]. Various materials available for laser fabrication are listedbelow-• GaInP   λ =670nm   Visible band• AlInP   λ=584 nm• Ternary AlGaAs (0.75-0.87µm• Quaternary  InGaAsP (1.1-1.6µm)• II-VI direct band gap: Hg CdTe • IV-VI direct band gap: PbSnTe ( λ=3-35 µm)We choose InGaAsP/InP material for our structure due to therelatively long emission wavelength and low nonradiativesurface recombination rate [6-7] of this material. Lownonradiative recombination rate is required for high gain.After choosing the material of our laser structure, thecomposition of different component in quaternary is to bedetermined. The direct energy gap E 0  (eV) of the quaternaryat room temperature is extrapolated from the ternary data andgiven by Moon et al [8].E0(x, y) = 1.35 + (0.758x + 0.642)x + (0.101y- 1.101)y -(0.28x - 0.109y + 0.159)xy            Fig (1). Bandgap vs. Lattice constant CurveFor a wavelength = 1.55 micron corresponding energy is0.8eV, we choose our x and y value which satisfy the aboveequation.Results are listed below-   x                                   y                           Quaternary              0.1                              0.59                  In 9.0 Ga 1.0 As 59.0 P 41.0  0.2                              0.67                  In 8.0 Ga 2.0 As 67.0 P 33.0  0.3                              0.76                  In 7.0 Ga 3.0 As 76.0 P 24.0  0.4                              0.86                  In 6.0 Ga 4.0 As 86.0 P 14.0  0.5                              0.96                  In 5.0 Ga 5.0 As 96.0 P 04.0On the basis of these calculations composition of strainedlayer of InGaAsP, which act as a quantum well, is taken asx=0.53 and y= 0.99.The critical layer thickness for InGaAsP layer is calculated byMatthews-Blakeslee [9] and People-Bean model [10]. According to Matthews-Blakeslee critical layer thickness isgiven by the expression-           ++−= 1lncos)1(4)cos1( 2bdfbd cc λνπθν Where b = burgers vector = 2fafa  is lattice parameter of InGaAsP film. ν = Poisson ratio, and == −ssfaaaf  misfit parameterAccording to People Bean model critical layer thickness isgiven by the expression- +−=bdfbd cc ln)1(32)1(2 νπνDesign Structure:   Fig (2). Layer Structure for Laser DeviceMultiple quantum well active layer is used between the N andP type InP layer. A square photonic crystal lattice is used inthe laser structure. An unstrained layer of InGaAsP acts asquantum barrier and compressively strained layer of InGaAsPacts as quantum well. Compressive strained layer [11] ofInGaAsP provides the following benefit  • Reduction of Auger recombination rate in device.• Reduction of transparency carrier density in laser.An unstrained layer of InGaAsP is lattice matched with InPsubstrate and for modeling and designing InGaAsP QWCs, itis important to know some fundamental properties of thematerial system InGaAsP such as lattice constant and band-gap as a function of composition. The lattice constant of thequaternary can be deduced from the well-known binarymaterials with the following values a 0 (GaAs) = 5.6533 A,a 0 ( (InP) = 5.8688 A, a 0 (GaP) = 5.4512 AVegard’s law, which states that the composition and latticeconstant have a linear relationship, holds for the quaternarymaterial system In x−1 Ga x As y P y−1 [12]. For any compositionof In x−1 Ga x As y P y−1  this gives a lattice constant ofa 0 (x, y) = 5.8688 - 0.4176x + 0.1896y + 0.0125xyFor the composition lattice-matched to the InP substrate, oneobtains a relationship of the composition fractions given by x =   yy0125.04176.01896.0−For the unstrained layer of InGaAsP which act as a quantum barrier, composition of InGaAsP is taken as =0.47 and y=0.94.  Simulation Result:The PBG structure used in our investigation is a 10×9 squarelattice of air columns each of which has an infinite lengthalong the y-axis. These air columns are surrounded byInGaAsP with a relative permittivity of 11.56. The cavitystructure is formed by removing one column of rods. Thistype of photonic structure favors TE mode while square latticeof dielectric columns embedded in air medium supports TMmode [13]. As the radius of air holes is increased, the TEmode gap frequency increases due to the reduction in effectivedielectric index of the medium and gap frequency variesinversely to square root of the dielectric of the medium.The aim is to design cavity for communication wavelength i.e.1.55µm. A value of inter-hole spacing, a, and radius of holes,r, is to find out to get maximum output and least scattering,provided width of the wave-guide should be of the order ofwavelength. The steps taken in the computation are as follows -1. Choose the wavelength for which cavity is to bedesigned.2. Starting value of cell size , a , can be taken a ≈2λ3. r = ma where 5.00 ≤< mWith starting value of cell size 0.775µ, one can vary the radiusof air columns in steps of 0.1µ and next simulation can beperformed for another value of cell size. With the choice ofλ=1.55 micron meter, one obtains a=1µm and r=0.3µm for theTE mode and a=1µm and r=0.35µm for the TM mode. Weformed the cavity by removing 2 air columns in X directionand 2 along Z direction. This PBG structure is twodimensional by design. We simulated for different set of cell size parameter withvariation in radius of holes for TM mode and TE modes.Simulation Results are presented below.  For TE Mode: radius of air column=0.3 µmCavity size =2 Χ  2    Unstrained InGaAsP         P InP layer  Unstrained InGaAsP      Strained InGaAsP  Unstrained InGaAsP   N InP Substrate      Strained InGaAsPFig (3). E y component of field for TE mode Refractive Index Profile:Fig (4). Refractive Index profile for TE modeFor TM Mode: Air column radius = 0.35 µm       and cell size parameter = 1.0 µm       Cavity size = 2 Χ 2;Fig (5). H y component of field for TM modeDiscussion:We have done simulation for different value of r/a=0.1, 0.2,0.3, 0.4 and 0.5µm and observed that most of the energy isconfined in the cavity for r/a =0.3µ in case of transverse electric mode, which is favored for air columns surrounded by dielectric medium. The fig (1) and fig (2) shows the variationof E y and refractive index profile for TE mode respectively while figure (3) shows the variation of H y for TM mode.   References[1] J.R.Cao, Po-Tsung Lee, Sang-Jun Choi, Roshanak Shafiiha, Seung-JuneChoi, John D. O’Brien, and P.Daniel Dapkus, “Nanofabrication ofPhotonic crystal membrane lasers” J.Vac.Sci.Technol.B 20(2002)[2] Richard W.Ziolkowski and Masahiro Tanaka, Optical and QuantumElectronics 31: 843-845, 1999[3] FDTD Manual [4] Taflov,A. Computational Electrodynamics, Artech House, Norwood,MA, 1995[5] Jelena Vuckovic, Marko Loncar, Hideo Mabuchi, and Axel Scherer,Phy.Rev. E, Vol 65, 016608[6] Painter et al.,”J.Opt.Soc.Am.B. Vol 16, Feb 1999.[7]    T. Baba, ‘‘Photonic crystals and micro diskcavities based on          GaInAsP-InP system,’’ IEEE J. Sel. TopicsQuantum Electron.          3, 808–830 (1997). [8]    R.L.Moon et al, J.Electron .Mater. 3, 635-644, 1974 [9]    J. W. Matthews and A. E. Blakeslee. Defects in epitaxial            multilayer. J. Crystal Growth 27, 118–125, 1974[10]   R. People and J. C. Bean. Calculation of critical layer thickness         versus lattice mismatch for GexSi1.x/Si strained-layer           heterostructures. Appl.Phys. Lett. 47(3), 322, 1985[11]    Y.Zhou et al., IEEE Photonics technol. Lett. 4, 1315 (1992)[12]  R. E. Nahory, M. A. Pollack, W. D. Johnston, Jr., and R. L. Barns.           Band gap versus composition and demonstration of Vegard’s law            For In1.xGaxAsyP1.y lattice matched to InP. Appl. Phys. Lett.            33(7), 659, 1978.[13]     J.D.Joannopoulos, R.D.Meade, and J.N.Winn Photonic crystal:            Molding the Flow of Light, Princeton University, Princeton, NJ            (1995).

Laser Fabrication by Using Photonic Crystal

http://dspace.mit.edu/bitstream/1721.1/3665/2/AMMNS016.pdf

Laser Fabrication by Using Photonic Crystal

Abstract

Similar works

Full text

Available Versions

DSpace@MIT