Simulation of visible and ultra-violet group-III nitride light emitting diodes

One-dimensional drift-diffusion model accounting for the unique properties of group-III nitrides is employed to simulate the carrier transport and radiative/non-radiative recombination of electrons and holes in light emitting diode heterostructures. Mixed finite-element method is used for numerical implementation of the model. The emission spectra are computed via the self-consistent solution of the Schrodinger-Poisson equations with account of complex valence band structure of nitride materials. Simulations of a number of single- and multiple-quantum well blue and ultraviolet light emitting diodes are presented and compared with available observations. Specific features of the III-nitride LED operation are considered in terms of modelling. Applicability of the drift-diffusion model to analysis of III-nitride LEDs is proved and still open questions are discussed.

[1]  J. Piprek.  Simulation of GaN-based Light-Emitting Devices , 2004 .

[2]  Timothy G. Trucano,et al.  Verification and Validation in Computational Fluid Dynamics , 2002 .

[3]  Shun Lien Chuang,et al.  k.p method for strained wurtzite semiconductors , 1996 .

[4]  D. Rose,et al.  Parameter Selection for Newton-Like Methods Applicable to Nonlinear Partial Differential Equations , 1980 .

[5]  Fernando Ponce,et al.  Measurement of the piezoelectric field across strained InGaN/GaN layers by electron holography , 1999 .

[6]  Oliver Ambacher,et al.  Evidence for nonlinear macroscopic polarization in III-V nitride alloy heterostructures , 2002 .

[7]  S. Laux,et al.  Monte Carlo analysis of electron transport in small semiconductor devices including band-structure and space-charge effects. , 1988, Physical review. B, Condensed matter.

[8]  Pierre Degond,et al.  Macroscopic models for semiconductor heterostructures , 1998 .

[9]  Les Hatton,et al.  The T-experiments: errors in scientific software , 1996, Quality of Numerical Software.

[10]  Joseph W. Jerome,et al.  A finite element approximation theory for the drift diffusion semiconductor model , 1991 .

[11]  Giovanni Ghione,et al.  Monte Carlo simulation of electron transport in the III-nitride wurtzite phase materials system: binaries and ternaries , 2001 .

[12]  Structural properties of the one-dimensional drift-diffusion models for semiconductors , 1996 .

[13]  S. Denbaars,et al.  Higher efficiency InGaN laser diodes with an improved quantum well capping configuration , 2002 .

[14]  Takashi Mukai,et al.  Spatial Inhomogeneity of Photoluminescence in an InGaN-Based Light-Emitting Diode Structure Probed by Near-Field optical Microscopy Under Illumination-Collection Mode , 2001 .

[15]  J W Orton,et al.  Group III nitride semiconductors for short wavelength light-emitting devices , 1998 .

[16]  Shuji Nakamura,et al.  Luminescence Spectra of Superbright Blue and Green InGaN/AlGaN/GaN Light-Emitting Diodes , 1996 .

[17]  Isamu Akasaki,et al.  Crystal Growth and Conductivity Control of Group III Nitride Semiconductors and Their Application to Short Wavelength Light Emitters , 1997 .

[18]  Qian Li,et al.  Error estimates in L2, H1 and Linfinity in covolume methods for elliptic and parabolic problems: A unified approach , 1999, Math. Comput..

[19]  H. Gummel.  A self-consistent iterative scheme for one-dimensional steady state transistor calculations , 1964 .

[20]  Hadis Morkoç,et al.  Progress and prospects of group-III nitride semiconductors , 1996 .

[21]  Donald Kershaw,et al.  Large-scale matrix problems and the numerical solution of partial differential equations , 1994 .

[22]  Oliver Ambacher,et al.  Determination of the Al mole fraction and the band gap bowing of epitaxial AlxGa1−xN films , 1997 .

[23]  Alfio Quarteroni,et al.  Current-voltage characteristics simulation of semiconductor devices using domain decomposition , 1995 .

[24]  N. Abdallah,et al.  Diffusion approximation for the one dimensional Boltzmann-Poisson system , 2004 .

[25]  Ansgar Jüngel,et al.  Quasi-hydrodynamic Semiconductor Equations , 2001 .

[26]  Xian-An Cao,et al.  Microstructural origin of leakage current in GaN/InGaN light-emitting diodes , 2004 .

[27]  James M. Ortega,et al.  Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[28]  Jin Seo Im,et al.  Radiative carrier lifetime, momentum matrix element, and hole effective mass in GaN , 1997 .

[29]  Christos Tsamis,et al.  Simulation of Semiconductor Processes and Devices 2001 , 2012 .

[30]  E. Allgower,et al.  Numerical path following , 1997 .

[31]  S. Nakamura.  InGaN/AlGaN blue-light-emitting diodes , 1995 .

[32]  K. Hess,et al.  Numerical simulation of wide band‐gap AlGaN/InGaN light‐emitting diodes for output power characteristics and emission spectra , 1996 .

[33]  Peter A. Markowich,et al.  A Singular Perturbation Analysis of the Fundamental Semiconductor Device Equations , 1984 .

[34]  Hyunsang Hwang,et al.  Effects of current spreading on the performance of GaN-based light-emitting diodes , 2001 .

[35]  M. R. Pinto,et al.  Carrier transport in laser heterostructures , 1994 .

[36]  A.-B. Chen,et al.  Theory of AlN, GaN, InN and their alloys , 1997 .

[37]  Y. Makarov,et al.  Carrier injection and light emission in visible and UV nitride LEDs by modeling , 2004 .

[38]  K. Bathe.  Finite Element Procedures , 1995 .

[39]  U. Tisch,et al.  Determination of Band‐Gap Bowing for AlxGa1–xN Alloys , 2001 .

[40]  Wil H. A. Schilders,et al.  Application of finite element methods to the simulation of semiconductor devices , 1999 .

[41]  Timothy G. Trucano,et al.  Verification and validation. , 2005 .

[42]  A. E. Boukili.  Arclength continuation methods and applications to 2D drift‐diffusion semiconductor equations , 1996 .

[43]  A. É. Yunovich,et al.  The Emission Properties of Light Emitting Diodes using InGaN/AlGaN/GaN Multiple Quantum Wells , 1998 .

[44]  Tanakorn Osotchan,et al.  Electron mobilities in gallium, indium, and aluminum nitrides , 1994 .

[45]  R. T. Webster,et al.  Temperature dependent transport properties in GaN, Al/sub x/Ga/sub 1-x/N, and In/sub x/Ga/sub 1-x/N semiconductors , 2001 .

[46]  Manijeh Razeghi,et al.  Determination of the band-gap energy of Al 12x In x N grown by metal-organic chemical-vapor deposition , 1997 .

[47]  M. S. Mock,et al.  On equations describing steady‐state carrier distributions in a semiconductor device , 1972 .

[48]  H. Morkoç,et al.  Energy band bowing parameter in AlxGa1-xN alloys , 2002 .

[49]  H. Gummel,et al.  Large-signal analysis of a silicon Read diode oscillator , 1969 .

[50]  O. Akcasu.  Convergence properties of Newton's method for the solution of the semiconductor transport equations and hybrid solution techniques for multidimensional simulation of VLSI devices , 1984 .

[51]  Patrick J. Roache,et al.  Verification and Validation in Computational Science and Engineering , 1998 .

[52]  R. Abram,et al.  Direct calculation of k.p parameters for wurtzite AlN, GaN and InN. , 2000 .

[53]  Jean Paul Freyssinier,et al.  Solid-state lighting: failure analysis of white LEDs , 2004 .

[54]  K. W. Kim,et al.  Design of white light-emitting diodes using InGaN/AlInGaN quantum-well structures , 2004 .

[55]  W. Fichtner,et al.  Numerical methods for semiconductor device simulation , 1983, IEEE Transactions on Electron Devices.

[56]  Wil H. A. Schilders,et al.  Uniform Numerical Methods for Problems with Initial and Boundary Layers , 1980 .

[57]  E. F. Schubert,et al.  Current crowding and optical saturation effects in GaInN/GaN light-emitting diodes grown on insulating substrates , 2001 .

[58]  Stephen M. Goodnick,et al.  Numerical challenges in particle-based approaches for the simulation of semiconductor devices , 2003, Math. Comput. Simul..

[59]  Y. Makarov,et al.  Modelling study of MQW LED operation , 2005 .

[60]  Robert Kaplar,et al.  Room-temperature direct current operation of 290 nm light-emitting diodes with milliwatt power levels , 2004 .

[61]  Wha Wil Schilders,et al.  Semiconductor device modelling from the numerical point of view , 1987 .

[62]  T. Moustakas,et al.  Thermal expansion of gallium nitride , 1994 .

[63]  D. N. De G. Allen,et al.  RELAXATION METHODS APPLIED TO DETERMINE THE MOTION, IN TWO DIMENSIONS, OF A VISCOUS FLUID PAST A FIXED CYLINDER , 1955 .

[64]  Oliver Ambacher,et al.  Growth and applications of Group III-nitrides , 1998 .

[65]  Guan-Ting Chen,et al.  Luminescence efficiency of InGaN multiple-quantum-well ultravioletlight-emitting diodes , 2004 .

[66]  Bo Monemar,et al.  Group III-nitride based hetero and quantum structures , 2000 .

[67]  Robert Bruce Lindsay,et al.  Physical Properties of Crystals , 1957 .

[68]  Shuji Nakamura,et al.  InGaN-based violet laser diodes , 1999 .

[69]  Siegfried Selberherr,et al.  Industrial application of heterostructure device simulation , 2001 .

[70]  A. N. Kovalev,et al.  Aging Mechanisms of InGaN/AlGaN/GaN Light-Emitting Diodes Operating at High Currents , 1998 .

[71]  M. Shur,et al.  Properties of advanced semiconductor materials : GaN, AlN, InN, BN, SiC, SiGe , 2001 .

[72]  Kevin F. Brennan,et al.  Theoretical study of the two-dimensional electron mobility in strained III-nitride heterostructures , 2001 .

[73]  W. V. Roosbroeck.  Theory of the flow of electrons and holes in germanium and other semiconductors , 1950 .

[74]  Sergey Yu. Karpov,et al.  Dislocation effect on light emission efficiency in gallium nitride , 2002 .

[75]  H. Grubin.  The physics of semiconductor devices , 1979, IEEE Journal of Quantum Electronics.

[76]  J. Slotboom.  Iterative scheme for 1- and 2- dimensional d.c.-transistor simulation , 1969 .

[77]  Xian-An Cao,et al.  Electrical characteristics of InGaN∕GaN light-emitting diodes grown on GaN and sapphire substrates , 2004 .

[78]  Y. T. Rebane,et al.  Influence of Poisson's ratio uncertainty on calculations of the bowing parameter for strained InGaN layers , 2001 .

[79]  Wladek Walukiewicz,et al.  Band gaps of InN and group III nitride alloys , 2003 .

[80]  A. Il'in.  Differencing scheme for a differential equation with a small parameter affecting the highest derivative , 1969 .

[81]  S. Nakamura,et al.  Candela‐class high‐brightness InGaN/AlGaN double‐heterostructure blue‐light‐emitting diodes , 1994 .