Design of Light Emitting Diodes (LED) - COMSOL.com

Excerpt from the Proceedings of the COMSOL Users Conference 2007 Grenoblewhere J ist the current density, V and V 2 thepotential in the two domains and n 1 and n 2 theideality factors.Figure 3 shows an example for the fitting result.The fitting quality is very good at low currentsand give the fitting parameters n 1 =2 and n 2 =1.2.Beyond 10mA the series resistance isdominating. This region can be modeled byCOMSOL.Current / A1,E+001,E-021,E-041,E-06measurementFit5. Comparison with the experiment5.1 2D-ModelingFig. 5 shows the excellent agreement of thesimulated and measured current-voltagecharacteristic (I-U- characteristic). Because mostmaterial parameters are not well known, one hasto vary the parameters so that the I-Ucharacteristicfits to the experimental result. Fig.5 also shows the I-U-characteristic of the p-njunction(fit). The difference between the purejunction characteristic and the measured I-Ucharacteristicresults from the series resistancedue to the contacts and the finite conductivity ofthe spreading layers.1,E-080,6 0,8 1 1,2 1,4 1,6 1,8Voltage / V1,00,8fitmeasurementFig. 3: fitting the current-voltage curve at lowcurrentscurrent / A0,60,4simulationThe next steps are straightforward: We have toenter the contact resistivities and theconductivities of the spreading layers. Only for a3-D-simulation we need a third domain for thecontact grid which defines the current-voltagecharacteristicbetween the contact grid and theupper spreading layer:J = ( V V2) / rho _ cont3−where J ist the current density, rho-cont thecontact resistance and V 3 and V 2 the potential inthe contact grid and the upper spreading layer,respectively. Fig. 4 shows an example of the 3-Dgeometric layout of the LED shown in fig. 2.electrical potential0,20,01 1,2 1,4 1,6 1,8voltage / VFig. 5: Current-voltage curve: small-current-fit,measurement and simulationFig. 6 shows the simulated current densitybetween two n-contacts (compare the schematicdrawing in fig. 1c) for three different n-spreadingconductivities together with the measuredradiation density. The current density must besimilar to the radiation density, therefore aqualitative comparison is allowed. Differencesare due to diffusion effects of the light within thechip. One can see a qualitative agreementbetween simulation and experiment.incoming current flowJ=(V3-V2)/rho_contincoming current flowJ=J01*exp(e*(V2-V)/(n1*kT))+J02*exp(e*(V2-V)/(n2*kT))8 x p-contactFig. 4: 3-D model of a LED

Excerpt from the Proceedings of the COMSOL Users Conference 2007 Grenoblecurrent density / a.u.1,00,80,60,40,2n-spreading 1n-spreading 2n-spreading 3measurement25020015010050light density / a.u.An appropriate parameter for a comparison withthe experiment is the voltage drop over the n-contact grid which can be easily measured withtwo probes. Fig. 7 shows the comparison of themeasured and simulated results. For optimumagreement the n-contact resistance had to beslightly reduced and the p-contact resistanceenhanced within a physically reasonable range.n-Kontaktp-Kontaktn-Kontakt0,00-54 -27 0 27 54locationFig. 6: Comparison of simulated current densityand measured radiation density5.2 3D-ModelingAfter fitting the material parameters with 2Dsimulations,one can continue with 3Dsimulations.131mV93mV6. Optimisation of a LED-structureFigure 8 shows the simulated current density inthe p-n-junction for different distances of two n-contact lines (different number of segments) anddifferent lateral distances of the n- and p-contact.The differences are significant. Configuration 1shows a very high current density near the n-contact (current crowding) and configuration 2 ahigh current density over a small area. The bestchoice is configuration 3 with a moderate currentdensity with a good homogeneity.149mV138mV45mV21150mV135mV93mVcurrent density3135mV98mV-54 -40,5 -27 -13,5 0 13,5 27 40,5 54location / µm160mV125mV58mVFig. 8: Simulated current density in the p-njunctionfor different geometric layouts164mV150mV109mVFig. 7: Simulated and measured voltage dropover the n-contact grid. The bondpad in theupper right corner is the reference pointAn example for a 3D-optimization is shown infigure 9. Here the current density in the p-njunctionfor a structure similar to that in figure 2(chip 1) and that of an optimized structure (chip2) are plotted. Chip 1 shows current crowdingaround the chip (near the n-contact) and adecreasing current density from the left to theright of the chip. Chip 2 shows less area withcurrent crowding and a better uniformity.

Excerpt from the Proceedings of the COMSOL Users Conference 2007 Grenoblechip 1chip 27. ConclusionsIn this paper a finite element model for thecurrent light intensity distribution across an LEDchip is presented. The model has beenimplemented in COMSOL Multiphysics, using atwo domain approach for the n- and p-layers wita boundary condition containing an effectivecurrent-voltage characteristic for the pn-junction.The simulated quantities are the current-voltagecharacteristic,the current distribution within theactive layer and the voltage drop on the contactgrid. The agreement between the simulated andexperimental results is very good. It is shownthat the uniformity of the current distribution inthe active region can be optimised significantlywith the help of the simulations.Fig. 9: Current density distribution in the p-njunctionfor two different chip designs